Why hyperbolic theories of dissipation cannot be ignored: Comments on a paper by Kostadt and Liu

Contrary to what is asserted in a recent paper by Kostadt and Liu ("Causality and stability of the relativistic diffusion equation"), experiments can tell apart (and in fact do) hyperbolic theories from parabolic theories of dissipation. It is stressed that the existence of a non--negligible relaxation time does not imply for the system to be out of the hydrodynamic regime.Comment: 8 pages Latex, to appear in Phys.Rev.

HIFI Spectroscopy of H2O{\rm H_2O} submm Lines in Nuclei of Actively Star Forming Galaxies

We present a systematic survey of multiple velocity-resolved H$_2$O spectra using Herschel/HIFI towards nine nearby actively star forming galaxies. The ground-state and low-excitation lines (E$_{\rm up}\,\le 130\,{\rm K}$) show profiles with emission and absorption blended together, while absorption-free medium-excitation lines ($130\,{\rm K}\, \le\, E_{\rm up}\,\le\,350\,{\rm K}$) typically display line shapes similar to CO. We analyze the HIFI observation together with archival SPIRE/PACS H$_2$O data using a state-of-the-art 3D radiative transfer code which includes the interaction between continuum and line emission. The water excitation models are combined with information on the dust- and CO spectral line energy distribution to determine the physical structure of the interstellar medium (ISM). We identify two ISM components that are common to all galaxies: A warm ($T_{\rm dust}\,\sim\,40-70\,{\rm K}$), dense ($n({\rm H})\,\sim\,10^5-10^6\,{\rm cm^{-3}}$) phase which dominates the emission of medium-excitation H$_2$O lines. This gas phase also dominates the FIR emission and the CO intensities for $J_{\rm up} > 8$. In addition a cold ($T_{\rm dust}\,\sim\,20-30\,{\rm K}$), dense ($n({\rm H})\sim\,10^4- 10^5\,{\rm cm^{-3}}$) more extended phase is present. It outputs the emission in the low-excitation H$_2$O lines and typically also produces the prominent line absorption features. For the two ULIRGs in our sample (Arp 220 and Mrk 231) an even hotter and more compact (R$_s\,\le\,100$ pc) region is present which is possibly linked to AGN activity. We find that collisions dominate the water excitation in the cold gas and for lines with $E_{\rm up}\le300\,{\rm K}$ and $E_{\rm up}\le800\,{\rm K}$ in the warm and hot component, respectively. Higher energy levels are mainly excited by IR pumping.Comment: Accepted by ApJ, in pres

Detecting the Most Distant (z>7) Objects with ALMA

Detecting and studying objects at the highest redshifts, out to the end of Cosmic Reionization at z>7, is clearly a key science goal of ALMA. ALMA will in principle be able to detect objects in this redshift range both from high-J (J>7) CO transitions and emission from ionized carbon, [CII], which is one of the main cooling lines of the ISM. ALMA will even be able to resolve this emission for individual targets, which will be one of the few ways to determine dynamical masses for systems in the Epoch of Reionization. We discuss some of the current problems regarding the detection and characterization of objects at high redshifts and how ALMA will eliminate most (but not all) of them.Comment: to appear in Astrophysics and Space Science, "Science with ALMA: a new era for Astrophysics", ed. R. Bachille

HIFI spectroscopy of low-level water transitions in M82

We present observations of the rotational ortho-water ground transition, the two lowest para-water transitions, and the ground transition of ionised ortho-water in the archetypal starburst galaxy M82, performed with the HIFI instrument on the Herschel Space Observatory. These observations are the first detections of the para-H2O(111-000) (1113\,GHz) and ortho-H2O+(111-000) (1115\,GHz) lines in an extragalactic source. All three water lines show different spectral line profiles, underlining the need for high spectral resolution in interpreting line formation processes. Using the line shape of the para-H2O(111-000) and ortho-H2O+(111-000) absorption profile in conjunction with high spatial resolution CO observations, we show that the (ionised) water absorption arises from a ~2000 pc^2 region within the HIFI beam located about ~50 pc east of the dynamical centre of the galaxy. This region does not coincide with any of the known line emission peaks that have been identified in other molecular tracers, with the exception of HCO. Our data suggest that water and ionised water within this region have high (up to 75%) area-covering factors of the underlying continuum. This indicates that water is not associated with small, dense cores within the ISM of M82 but arises from a more widespread diffuse gas component.Comment: 5 pages, 4 figures. Accepted for publication in A&

Molecular gas in high-velocity clouds: revisited scenario

We report a new search for 12CO(1-0) emission in high-velocity clouds (HVCs) performed with the IRAM 30 m telescope. This search was motivated by the recent detection of cold dust emission in the HVCs of Complex C. Despite a spatial resolution which is three times better and sensitivity twice as good compared to previous studies, no CO emission is detected in the HVCs of Complex C down to a best 5 sigma limit of 0.16 K km/s at a 22'' resolution. The CO emission non-detection does not provide any evidence in favor of large amounts of molecular gas in these HVCs and hence in favor of the infrared findings. We discuss different configurations which, however, allow us to reconcile the negative CO result with the presence of molecular gas and cold dust emission. H2 column densities higher than our detection limit, N(H2) = 3x10^{19} cm^{-2}, are expected to be confined in very small and dense clumps with 20 times smaller sizes than the 0.5 pc clumps resolved in our observations according to the results obtained in cirrus clouds, and might thus still be highly diluted. As a consequence, the inter-clump gas at the 1 pc scale has a volume density lower than 20 cm^{-3} and already appears as too diffuse to excite the CO molecules. The observed physical conditions in the HVCs of Complex C also play an important role against CO emission detection. It has been shown that the CO-to-H2 conversion factor in low metallicity media is 60 times higher than at the solar metallicity, leading for a given H2 column density to a 60 times weaker integrated CO intensity. And the very low dust temperature estimated in these HVCs implies the possible presence of gas cold enough (< 20 K) to cause CO condensation onto dust grains under interstellar medium pressure conditions and thus CO depletion in gas-phase observations.Comment: 9 pages, 4 figures, Accepted for publication in A&

The very red afterglow of GRB 000418 - further evidence for dust extinction in a GRB host galaxy

We report near-infrared and optical follow-up observations of the afterglow of the Gamma-Ray Burst 000418 starting 2.5 days after the occurrence of the burst and extending over nearly seven weeks. GRB 000418 represents the second case for which the afterglow was initially identified by observations in the near-infrared. During the first 10 days its R-band afterglow was well characterized by a single power-law decay with a slope of 0.86. However, at later times the temporal evolution of the afterglow flattens with respect to a simple power-law decay. Attributing this to an underlying host galaxy we find its magnitude to be R=23.9 and an intrinsic afterglow decay slope of 1.22. The afterglow was very red with R-K=4 mag. The observations can be explained by an adiabatic, spherical fireball solution and a heavy reddening due to dust extinction in the host galaxy. This supports the picture that (long) bursts are associated with events in star-forming regions.Comment: Accepted for publication in The Astrophysical Journal. 12 pages; citations & references updated; minor textual change

Stochastic dynamics of correlations in quantum field theory: From Schwinger-Dyson to Boltzmann-Langevin equation

The aim of this paper is two-fold: in probing the statistical mechanical properties of interacting quantum fields, and in providing a field theoretical justification for a stochastic source term in the Boltzmann equation. We start with the formulation of quantum field theory in terms of the Schwinger - Dyson equations for the correlation functions, which we describe by a closed-time-path master ($n = \infty PI$) effective action. When the hierarchy is truncated, one obtains the ordinary closed-system of correlation functions up to a certain order, and from the nPI effective action, a set of time-reversal invariant equations of motion. But when the effect of the higher order correlation functions is included (through e.g., causal factorization-- molecular chaos -- conditions, which we call 'slaving'), in the form of a correlation noise, the dynamics of the lower order correlations shows dissipative features, as familiar in the field-theory version of Boltzmann equation. We show that fluctuation-dissipation relations exist for such effectively open systems, and use them to show that such a stochastic term, which explicitly introduces quantum fluctuations on the lower order correlation functions, necessarily accompanies the dissipative term, thus leading to a Boltzmann-Langevin equation which depicts both the dissipative and stochastic dynamics of correlation functions in quantum field theory.Comment: LATEX, 30 pages, no figure

Mapping the cold dust temperatures and masses of nearby Kingfish galaxies with Herschel

Taking advantage of the sensitivity and angular resolution of the Herschel Space Observatory at far-infrared and submm wavelengths, we aim to characterize the physical properties of cold dust within nearby galaxies and study the robustness of the parameters we derive using different modified blackbody models. For a pilot subsample of the KINGFISH program, we perform 2 temperature fits of the Spitzer and Herschel photometric data (24 to 500um), with a warm and a cold component, globally and in each resolution element.At global scales, we observe ranges of values for beta_c(0.8 to 2.5) and Tc(19.1 to 25.1K).We compute maps of our parameters with beta fixed or free to test the robustness of the temperature and dust surface density maps we deduce. When the emissivity is fixed, we observe temperature gradients as a function of radius.When the emissivity is fitted as a free parameter, barred galaxies tend to have uniform fitted emissivities.Gathering resolved elements in a Tc-beta_c diagram underlines an anti-correlation between the two parameters.It remains difficult to assess whether the dominant effect is the physics of dust grains, noise, or mixing along the line of sight and in the beam. We finally observe in both cases that the dust column density peaks in central regions of galaxies and bar ends (coinciding with molecular gas density enhancements usually found in these locations).We also quantify how the total dust mass varies with our assumptions about the emissivity index as well as the influence of the wavelength coverage used in the fits. We show that modified blackbody fits using a shallow emissivity (beta_c < 2.0) lead to significantly lower dust masses compared to the beta_c < 2.0 case, with dust masses lower by up to 50% if beta_c=1.5 for instance.The working resolution affects our total dust mass estimates: masses increase from global fits to spatially-resolved fits.Comment: 26 pages, 12 figures, 4 tables, accepted for publication in MNRAS, 2012 June 2

Optimal designs for rational function regression

We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The proposed method treats D-, E-, A-, and $\Phi_p$-optimal designs in a unified manner, and generates a polynomial whose zeros are the support points of the optimal approximate design, generalizing a number of previously known results of the same flavor. The method is based on a mathematical optimization model that can incorporate various criteria of optimality and can be solved efficiently by well established numerical optimization methods. In contrast to previous optimization-based methods proposed for similar design problems, it also has theoretical guarantee of its algorithmic efficiency; in fact, the running times of all numerical examples considered in the paper are negligible. The stability of the method is demonstrated in an example involving high degree polynomials. After discussing linear models, applications for finding locally optimal designs for nonlinear regression models involving rational functions are presented, then extensions to robust regression designs, and trigonometric regression are shown. As a corollary, an upper bound on the size of the support set of the minimally-supported optimal designs is also found. The method is of considerable practical importance, with the potential for instance to impact design software development. Further study of the optimality conditions of the main optimization model might also yield new theoretical insights.Comment: 25 pages. Previous version updated with more details in the theory and additional example

Stochastic semiclassical gravity

In the first part of this paper, we show that the semiclassical Einstein-Langevin equation, introduced in the framework of a stochastic generalization of semiclassical gravity to describe the back reaction of matter stress-energy fluctuations, can be formally derived from a functional method based on the influence functional of Feynman and Vernon. In the second part, we derive a number of results for background solutions of semiclassical gravity consisting of stationary and conformally stationary spacetimes and scalar fields in thermal equilibrium states. For these cases, fluctuation-dissipation relations are derived. We also show that particle creation is related to the vacuum stress-energy fluctuations and that it is enhanced by the presence of stochastic metric fluctuations.Comment: 26 pages, RevTeX, no figure