Monte Carlo simulation of particle interactions at high dynamic range: Advancing beyond the Googol

We present a method which extends Monte Carlo studies to situations that require a large dynamic range in particle number. The underlying idea is that, in order to calculate the collisional evolution of a system, some particle interactions are more important than others and require more resolution, while the behavior of the less important, usually of smaller mass, particles can be considered collectively. In this approximation groups of identical particles, sharing the same mass and structural parameters, operate as one unit. The amount of grouping is determined by the zoom factor -- a free parameter that determines on which particles the computational effort is focused. Two methods for choosing the zoom factors are discussed: the `equal mass method,' in which the groups trace the mass density of the distribution, and the `distribution method,' which additionally follows fluctuations in the distribution. Both methods achieve excellent correspondence with analytic solutions to the Smoluchowski coagulation equation. The grouping method is furthermore applied to simulations involving runaway kernels, where the particle interaction rate is a strong function of particle mass, and to situations that include catastrophic fragmentation. For the runaway simulations previous predictions for the decrease of the runaway timescale with the initial number of particles ${\cal N}$ are reconfirmed, extending ${\cal N}$ to $10^{160}$. Astrophysical applications include modeling of dust coagulation, planetesimal accretion, and the dynamical evolution of stars in large globular clusters. The proposed method is a powerful tool to compute the evolution of any system where the particles interact through discrete events, with the particle properties characterized by structural parameters.Comment: 18 pages, 10 figures. Re-submitted to ApJ with comments of the referee include

The nature of the ISM in galaxies during the star-formation activity peak of the Universe

We combine a semi-analytic model of galaxy formation, tracking atomic and molecular phases of cold gas, with a three-dimensional radiative-transfer and line tracing code to study the sub-mm emission from atomic and molecular species (CO, HCN, [CI], [CII], [OI]) in galaxies. We compare the physics that drives the formation of stars at the epoch of peak star formation (SF) in the Universe (z = 2.0) with that in local galaxies. We find that normal star-forming galaxies at high redshift have much higher CO-excitation peaks than their local counterparts and that CO cooling takes place at higher excitation levels. CO line ratios increase with redshift as a function of galaxy star-formation rate, but are well correlated with H2 surface density independent of redshift. We find an increase in the [OI]/[CII] line ratio in typical star-forming galaxies at z = 1.2 and z = 2.0 with respect to counterparts at z = 0. Our model results suggest that typical star-forming galaxies at high redshift consist of much denser and warmer star-forming clouds than their local counterparts. Galaxies belonging to the tail of the SF activity peak at z = 1.2 are already less dense and cooler than counterparts during the actual peak of SF activity (z = 2.0). We use our results to discuss how future ALMA surveys can best confront our predictions and constrain models of galaxy formation.Comment: 19 pages, 14 figures, accepted for publication in MNRA

Effects of turbulence and rotation on protostar formation as a precursor to seed black holes

Context. The seeds of the first supermassive black holes may have resulted from the direct collapse of hot primordial gas in $\gtrsim 10^4$ K haloes, forming a supermassive or quasistar as an intermediate stage. Aims. We explore the formation of a protostar resulting from the collapse of primordial gas in the presence of a strong Lyman-Werner radiation background. Particularly, we investigate the impact of turbulence and rotation on the fragmentation behaviour of the gas cloud. We accomplish this goal by varying the initial turbulent and rotational velocities. Methods. We performed 3D adaptive mesh refinement simulations with a resolution of 64 cells per Jeans length using the ENZO code, simulating the formation of a protostar up to unprecedentedly high central densities of $10^{21}$ cm$^{-3}$, and spatial scales of a few solar radii. To achieve this goal, we employed the KROME package to improve modelling of the chemical and thermal processes. Results. We find that the physical properties of the simulated gas clouds become similar on small scales, irrespective of the initial amount of turbulence and rotation. After the highest level of refinement was reached, the simulations have been evolved for an additional ~5 freefall times. A single bound clump with a radius of $2 \times 10^{-2}$ AU and a mass of ~$7 \times 10^{-2}$ M$_{\odot}$ is formed at the end of each simulation, marking the onset of protostar formation. No strong fragmentation is observed by the end of the simulations, regardless of the initial amount of turbulence or rotation, and high accretion rates of a few solar masses per year are found. Conclusions. Given such high accretion rates, a quasistar of $10^5$ M$_{\odot}$ is expected to form within $10^5$ years.Comment: 18 pages, 7 figures, fixed typos, added references and clarified some details; accepted for publication in A&

A UV flux constraint on the formation of direct collapse black holes

The ability of metal free gas to cool by molecular hydrogen in primordial halos is strongly associated with the strength of ultraviolet (UV) flux produced by the stellar populations in the first galaxies. Depending on the stellar spectrum, these UV photons can either dissociate $\rm H_{2}$ molecules directly or indirectly by photo-detachment of $\rm H^{-}$ as the latter provides the main pathway for $\rm H_{2}$ formation in the early universe. In this study, we aim to determine the critical strength of the UV flux above which the formation of molecular hydrogen remains suppressed for a sample of five distinct halos at $z>10$ by employing a higher order chemical solver and a Jeans resolution of 32 cells. We presume that such flux is emitted by PopII stars implying atmospheric temperatures of $\rm 10^{4}$~K. We performed three-dimensional cosmological simulations and varied the strength of the UV flux below the Lyman limit in units of $\rm J_{21}$. Our findings show that the value of $\rm J_{21}^{crit}$ varies from halo to halo and is sensitive to the local thermal conditions of the gas. For the simulated halos it varies from 400-700 with the exception of one halo where $\rm J_{21}^{crit} \geq 1500$. This has important implications for the formation of direct collapse black holes and their estimated population at z > 6. It reduces the number density of direct collapse black holes by almost three orders of magnitude compared to the previous estimates.Comment: 10 pages, 6 figures, matches the accepted version to ber published in MNRAS, higher resolution version is available at http://www.astro.physik.uni-goettingen.de/~mlatif/Jcrit.pd

The formation of supermassive black holes in the first galaxies

We discuss the formation of supermassive black holes in the early universe, and how to probe their subsequent evolution with the upcoming mm/sub-mm telescope ALMA. We first focus on the chemical and radiative conditions for black hole formation, in particular considering radiation trapping and molecular dissociation effects. We then turn our attention towards the magnetic properties in the halos where the first black holes form, and show that the presence of turbulence may lead to a magnetic dynamo, which could support the black hole formation process by providing an efficient means of transporting the angular momentum. We finally focus on observable properties of high-redshift black holes with respect to ALMA, and discuss how to distinguish between chemistry driven by the starburst and chemistry driven by X-rays from the black hole.Comment: Contribution to AIP conference proceedings "First Stars and Galaxies: Challenges in the Next Decade". 4 pages, 3 figure

Search for Interstellar Water in the Translucent Molecular Cloud toward HD 154368

We report an upper limit of 9 x 10^{12} cm-2 on the column density of water in the translucent cloud along the line of sight toward HD 154368. This result is based upon a search for the C-X band of water near 1240 \AA carried out using the Goddard High Resolution Spectrograph of the Hubble Space Telescope. Our observational limit on the water abundance together with detailed chemical models of translucent clouds and previous measurements of OH along the line of sight constrain the branching ratio in the dissociative recombination of H_3O+ to form water. We find at the $3\sigma$ level that no more than 30% of dissociative recombinations of H_3O+ can lead to H_2O. The observed spectrum also yielded high-resolution observations of the Mg II doublet at 1239.9 \AA and 1240.4 \AA, allowing the velocity structure of the dominant ionization state of magnesium to be studied along the line of sight. The Mg II spectrum is consistent with GHRS observations at lower spectral resolution that were obtained previously but allow an additional velocity component to be identified.Comment: Accepted by ApJ, uses aasp

Development of a novel forward dynamic programming method for weather routing

This paper presents a novel forward dynamic programming method for weather routing to minimise ship fuel consumption during a voyage. Compared with traditional weather routing methods which only optimise the ship's heading, while the engine power or propeller rotation speed is set as a constant throughout the voyage, this new method considers both the ship power settings and heading controls. A float state technique is used to reduce the iterations required during optimisation and thus save computation time. This new method could lead to quasiglobal optimal routing in comparison with the traditional weather routing methods

Uncertainties in water chemistry in disks: An application to TW Hya

Context. This paper discusses the sensitivity of water lines to chemical processes and radiative transfer for the protoplanetary disk around TW Hya. The study focuses on the Herschel spectral range in the context of new line detections with the PACS instrument from the Gas in Protoplanetary Systems project (GASPS). Aims. The paper presents an overview of the chemistry in the main water reservoirs in the disk around TW Hya. It discusses the limitations in the interpretation of observed water line fluxes. Methods. ... (abbreviated) Results. We report new line detections of p-H2O (3_22-2_11) at 89.99 micron and CO J=18-17 at 144.78 micron for the disk around TW Hya. Disk modeling shows that the far-IR fine structure lines ([OI], [CII]) and molecular submm lines are very robust to uncertainties in the chemistry, while the water line fluxes can change by factors of a few. The water lines are optically thick, sub-thermally excited and can couple to the background continuum radiation field. The low-excitation water lines are also sensitive to uncertainties in the collision rates, e.g. with neutral hydrogen. The gas temperature plays an important role for the [OI] fine structure line fluxes, the water line fluxes originating from the inner disk as well as the high excitation CO, CH+ and OH lines. Conclusions. Due to their sensitivity on chemical input data and radiative transfer, water lines have to be used cautiously for understanding details of the disk structure. Water lines covering a wide range of excitation energies provide access to the various gas phase water reservoirs (inside and outside the snow line) in protoplanetary disks and thus provide important information on where gas-phase water is potentially located. Experimental and/or theoretical collision rates for H2O with atomic hydrogen are needed to diminish uncertainties from water line radiative transfer.Comment: accepted for publication in A&

The Abundance and Emission of H2O and O2 in Clumpy Molecular Clouds

Recent observations with the Submillimeter Wave Astronomy Satellite indicate abundances of gaseous H2O and O2 in dense molecular clouds which are significantly lower than found in standard homogeneous chemistry models. We present here results for the thermal and chemical balance of inhomogeneous molecular clouds exposed to ultraviolet radiation in which the abundances of H2O and O2 are computed for various density distributions, radiation field strengths and geometries. It is found that an inhomogeneous density distribution lowers the column densities of H2O and O2 compared to the homogeneous case by more than an order of magnitude at the same A_V. O2 is particularly sensitive to the penetrating ultraviolet radiation, more so than H2O. The S140 and rho Oph clouds are studied as relevant test cases of star-forming and quiescent regions. The SWAS results of S140 can be accommodated naturally in a clumpy model with mean density of 2x10^3 cm-3 and enhancement I_UV=140 compared with the average interstellar radiation field, in agreement with observations of [CI] and 13CO of this cloud. Additional radiative transfer computations suggest that this diffuse H2O component is warm, ~60-90 K, and can account for the bulk of the 1_10-1_01 line emission observed by SWAS. The rho Oph model yields consistent O2 abundances but too much H2O, even for [C]/[O]=0.94, if I_UV<10 respectively <40 for a mean density of 10^3 respectively 10^4 cm-3. It is concluded that enhanced photodissociation in clumpy regions can explain the low H2O and O2 abundances and emissivities found in the large SWAS beam for extended molecular clouds, but that additional freeze-out of oxygen onto grains is needed in dense cold cores.Comment: To be published in ApJ