Eigenvector Model Descriptors for Solving an Inverse Problem of Helmholtz Equation: Extended Materials

We study the seismic inverse problem for the recovery of subsurface properties in acoustic media. In order to reduce the ill-posedness of the problem, the heterogeneous wave speed parameter to be recovered is represented using a limited number of coefficients associated with a basis of eigenvectors of a diffusion equation, following the regularization by discretization approach. We compare several choices for the diffusion coefficient in the partial differential equations, which are extracted from the field of image processing. We first investigate their efficiency for image decomposition (accuracy of the representation with respect to the number of variables and denoising). Next, we implement the method in the quantitative reconstruction procedure for seismic imaging, following the Full Waveform Inversion method, where the difficulty resides in that the basis is defined from an initial model where none of the actual structures is known. In particular, we demonstrate that the method is efficient for the challenging reconstruction of media with salt-domes. We employ the method in two and three-dimensional experiments and show that the eigenvector representation compensates for the lack of low frequency information, it eventually serves us to extract guidelines for the implementation of the method.Comment: 45 pages, 37 figure

The Implications of Gunn-Peterson Troughs in the HeII Lyman-alpha Forest

Many experts believe that the z ~ 3 HeII Ly-alpha forest will suffer from the same saturation issues as the z ~ 6 HI Ly-alpha forest and, therefore, will not be a sensitive probe of HeII reionization. However, there are several factors that make HeII Ly-alpha absorption more sensitive than HI Ly-alpha. We show that observations of HeII Ly-alpha and Ly-beta Gunn-Peterson troughs can provide a relatively model-independent constraint on the volume-averaged HeII fraction of x_HeII >~ 0.1. This bound derives from first using the most underdense regions in the HeII forest to constrain the local HeII fraction and, then, assuming photoionization equilibrium with the maximum allowed photoionization rate to calculate the ionization state of nearby gas. It is possible to evade this constraint by a factor of ~2, but only if the HeII were reionized recently. We argue that HeII Ly-alpha Gunn-Peterson troughs observed in the spectra of Q0302-003 and HE2347-4342 signify the presence of >~ 10 comoving Mpc patches in which x_HeII > 0.03. This is a factor of 20 improvement over previous constraints from these spectra and 100 times stronger than the tightest constraint on the HI volume-filling fraction from the z>6 HI Lyman forest.Comment: 5 pages, 4 figures, includes some supplementary text not in ApJ Letter versio

Radiative cooling of swept up gas in AGN-driven galactic winds and its implications for molecular outflows

We recently used hydro-chemical simulations to demonstrate that molecular outflows observed in luminous quasars can be explained by molecule formation within the AGN wind. However, these simulations cover a limited parameter space, due to their computational cost. We have therefore developed an analytic model to follow cooling in the shocked ISM layer of an AGN wind. We explore different ambient densities ($1-10^{4} \, \rm{cm}^{-3}$), density profile slopes ($0-1.5$), AGN luminosities ($10^{44}-10^{47} \, \rm{erg} \, \rm{s}^{-1}$), and metallicities ($0.1-3 \rm{Z}_{\odot}$). The swept up gas mostly cools within ~1 Myr. Based on our previous simulations, we predict that this gas would produce observable molecular outflows. The instantaneous momentum boost initially increases as the outflow decelerates. However, it reaches a maximum of $\approx$20, due to work done against the gravitational potential. The predicted time-averaged observational estimate of the molecular outflow momentum boost reaches a maximum of $\approx1-2$, partly due to our assumed molecular fraction, 0.2, but also because the instantaneous and observational, time-averaged definitions are not equivalent. Thus recent observational estimates of order unity momentum boosts do not necessarily rule out energy-driven outflows. Finally, we find that dust grains are likely to re-form by accretion of metals after the shocked ISM layer has cooled, assuming that a small fraction of dust grains swept up after this layer has cooled are able to mix into the cool phase, and assuming that grain growth remains efficient in the presence of the strong AGN radiation field. This would enable rapid molecule formation, as assumed in our models.Comment: 22 pages, 16 figures (including appendices). Accepted for publication in MNRA

The origin of fast molecular outflows in quasars: molecule formation in AGN-driven galactic winds

We explore the origin of fast molecular outflows that have been observed in Active Galactic Nuclei (AGN). Previous numerical studies have shown that it is difficult to create such an outflow by accelerating existing molecular clouds in the host galaxy, as the clouds will be destroyed before they can reach the high velocities that are observed. In this work, we consider an alternative scenario where molecules form in-situ within the AGN outflow. We present a series of hydro-chemical simulations of an isotropic AGN wind interacting with a uniform medium. We follow the time-dependent chemistry of 157 species, including 20 molecules, to determine whether molecules can form rapidly enough to produce the observed molecular outflows. We find H$_2$ outflow rates up to 140 M$_\odot$ yr$^{-1}$, which is sensitive to density, AGN luminosity, and metallicity. We compute emission and absorption lines of CO, OH and warm (a few hundred K) H$_2$ from the simulations in post-processing. The CO-derived outflow rates and OH absorption strengths at solar metallicity agree with observations, although the maximum line of sight velocities from the model CO spectra are a factor $\approx$2 lower than is observed. We derive a CO (1-0) to H$_2$ conversion factor of $\alpha_{\rm{CO} (1-0)}$ = 0.13 M$_\odot$ (K km s$^{-1}$ pc$^2$)$^{-1}$, 6 times lower than is commonly assumed in observations of such systems. We find strong emission from the mid-infrared lines of H$_2$. The mass of H$_2$ traced by this infrared emission is within a few per cent of the total H$_2$ mass. This H$_2$ emission may be observable by JWST.Comment: 30 pages, 21 figures (including appendices), resubmitted to MNRAS following referee's report. Some results have changed from the previous version, in particular for warm H2 emission (see Figs. 5 and 13

A Direct Measurement of the IGM Opacity to HI Ionizing Photons

We present a new method to directly measure the opacity from HI Lyman limit (LL) absorption k_LL along quasar sightlines by the intergalactic medium (IGM). The approach analyzes the average (``stacked'') spectrum of an ensemble of quasars at a common redshift to infer the mean free path (MFP) to ionizing radiation. We apply this technique to 1800 quasars at z=3.50-4.34 drawn from the Sloan Digital Sky Survey (SDSS), giving the most precise measurements on k_LL at any redshift. From z=3.6 to 4.3, the opacity increases steadily as expected and is well parameterized by MFP = (48.4 +/- 2.1) - (38.0 +/- 5.3)*(z-3.6) h^-1 Mpc (proper distance). The relatively high MFP values indicate that the incidence of systems which dominate k_LL evolves less strongly at z>3 than that of the Lya forest. We infer a mean free path three times higher than some previous estimates, a result which has important implications for the photo-ionization rate derived from the emissivity of star forming galaxies and quasars. Finally, our analysis reveals a previously unreported, systematic bias in the SDSS quasar sample related to the survey's color targeting criteria. This bias potentially affects all z~3 IGM studies using the SDSS database.Comment: 7 pages, 4 figures; Accepted to ApJ

Effects of Ultraviolet Background and Local Stellar Radiation on the H_I Column Density Distribution

We study the impact of ultraviolet background (UVB) radiation field and the local stellar radiation on the H_I column density distribution f(N_HI) of damped Ly-alpha systems (DLAs) and sub-DLAs at z=3 using cosmological smoothed particle hydrodynamics simulations. We find that, in the previous simulations with an optically thin approximation, the UVB was sinking into the H_I cloud too deeply, and therefore we underestimated the f(N_HI) at 19 < log(N_HI) < 21.2 compared to the observations. If the UVB is shut off in the high-density regions with n_gas > 6 x 10^{-3} cm^{-3}, then we reproduce the observed f(N_HI) at z=3 very well. We also investigate the effect of local stellar radiation by post-processing our simulation with a radiative transfer code, and find that the local stellar radiation does not change the f(N_HI) very much. Our results show that the shape of f(N_HI) is determined primarily by the UVB with a much weaker effect by the local stellar radiation and that the optically thin approximation often used in cosmological simulation is inadequate to properly treat the ionization structure of neutral gas in and out of DLAs. Our result also indicates that the DLA gas is closely related to the transition region from optically-thick neutral gas to optically-thin ionized gas within dark matter halos.Comment: 5 pages, 3 figures, uses emulateapj. ApJL in press. Corrected a plotting error in Fig. 3, which reduced the effect of local stellar radiation on f(N_HI