arXiv subjects

M. Spaans

Publications and source records attributed to M. Spaans.

At least 73 records · Page 4Linked to original sources

arXiv2012

The implications of dust for high-redshift protogalaxies and the formation of binary disks

Numerical simulations suggest that the first galaxies are formed in protogalactic halos with virial temperatures >= 10^4 K. It is likely that such halos are polluted with trace amounts of metals produced by the first generation of stars. The presence of dust can significantly change the chemistry and dynamics of early galaxies. In this article, we aim to assess the role of dust on the thermal and dynamical evolution of the first galaxies in the presence of a background UV flux, and its implications for the observability of Lyman alpha emitters and sub-mm sources. We have performed high resolution cosmological simulations using the adaptive mesh refinement code FLASH to accomplish this goal. We have developed a chemical network appropriate for these conditions and coupled it with the FLASH code. The main ingredients of our chemical model include the formation of molecules, a multi-level treatment of atomic hydrogen, line trapping of Lyman alpha photons and, photoionization and photodissociation processes in a UV background. We found that the formation of molecules (H_{2} and HD) is significantly enhanced in the presence of dust grains. The presence of a background UV flux strongly influences the formation of molecules by photodissociating them. We explore the evolution after a major merger, leading to the formation of a binary disk. These disks have gas masses of ~10^{7} M_sun at a redshift of 5.4. Each disk lies in a separate subhalo as a result of the merger event. The disks are supported by turbulent pressure due to the highly supersonic turbulence present in the halo. The presence of dust does not significantly reduce the Lyman alpha emission. The emission of Lyman alpha is extended and originates from the envelope of the halo due to line trapping effects. We also find that dust masses of 10^8 M_sun are required to observe the dust continuum emission from z 5 galaxies with ALMA.

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arXiv2012

Diagnostics of the Molecular Component of PDRs with Mechanical Heating

Context. Multitransition CO observations of galaxy centers have revealed that significant fractions of the dense circumnuclear gas have high kinetic temperatures, which are hard to explain by pure photon excitation, but may be caused by dissipation of turbulent energy. Aims. We aim to determine to what extent mechanical heating should be taken into account while modelling PDRs. To this end, the effect of dissipated turbulence on the thermal and chemical properties of PDRs is explored. Methods. Clouds are modelled as 1D semi-infinite slabs whose thermal and chemical equilibrium is solved for using the Leiden PDR-XDR code. Results. In a steady-state treatment, mechanical heating seems to play an important role in determining the kinetic temperature of the gas in molecular clouds. Particularly in high-energy environments such as starburst galaxies and galaxy centers, model gas temperatures are underestimated by at least a factor of two if mechanical heating is ignored. The models also show that CO, HCN and H2 O column densities increase as a function of mechanical heating. The HNC/HCN integrated column density ratio shows a decrease by a factor of at least two in high density regions with n \sim 105 cm-3, whereas that of HCN/HCO+ shows a strong dependence on mechanical heating for this same density range, with boosts of up to three orders of magnitude. Conclusions. The effects of mechanical heating cannot be ignored in studies of the molecular gas excitation whenever the ratio of the star formation rate to the gas density is close to, or exceeds, 7 \times 10-6 M yr-1 cm4.5 . If mechanical heating is not included, predicted column densities are underestimated, sometimes even by a few orders of magnitude. As a lower bound to its importance, we determined that it has non-negligible effects already when mechanical heating is as little as 1% of the UV heating in a PDR.

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arXiv2011

Gas modelling in the disc of HD 163296

We present detailed model fits to observations of the disc around the Herbig Ae star HD 163296. This well-studied object has an age of ~ 4 Myr, with evidence of a circumstellar disc extending out to ~ 540AU. We use the radiation thermo-chemical disc code ProDiMo to model the gas and dust in the circumstellar disc of HD 163296, and attempt to determine the disc properties by fitting to observational line and continuum data. These include new Herschel/PACS observations obtained as part of the open-time key program GASPS (Gas in Protoplanetary Systems), consisting of a detection of the [OI]63mic line and upper limits for several other far infrared lines. We complement this with continuum data and ground-based observations of the 12CO 3-2, 2-1 and 13CO J=1-0 line transitions, as well as the H2 S(1) transition. We explore the effects of stellar ultraviolet variability and dust settling on the line emission, and on the derived disc properties. Our fitting efforts lead to derived gas/dust ratios in the range 9-100, depending on the assumptions made. We note that the line fluxes are sensitive in general to the degree of dust settling in the disc, with an increase in line flux for settled models. This is most pronounced in lines which are formed in the warm gas in the inner disc, but the low excitation molecular lines are also affected. This has serious implications for attempts to derive the disc gas mass from line observations. We derive fractional PAH abundances between 0.007 and 0.04 relative to ISM levels. Using a stellar and UV excess input spectrum based on a detailed analysis of observations, we find that the all observations are consistent with the previously assumed disc geometry.

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arXiv2011

Enhanced H2O formation through dust grain chemistry in X-ray exposed environments

The ULIRG Mrk 231 exhibits very strong water rotational lines between λ= 200-670μm, comparable to the strength of the CO rotational lines. High redshift quasars also show similar CO and H2O line properties, while starburst galaxies, such as M82, lack these very strong H2O lines in the same wavelength range, but do show strong CO lines. We explore the possibility of enhancing the gas phase H2O abundance in X-ray exposed environments, using bare interstellar carbonaceous dust grains as a catalyst. Cloud-cloud collisions cause C and J shocks, and strip the grains of their ice layers. The internal UV field created by X-rays from the accreting black hole does not allow to reform the ice. We determine formation rates of both OH and H2O on dust grains, having temperature T_dust=10-60 K, using both Monte Carlo as well as rate equation method simulations. The acquired formation rates are added to our X-ray chemistry code, that allows us to calculate the thermal and chemical structure of the interstellar medium near an active galactic nucleus. We derive analytic expressions for the formation of OH and H2O on bare dust grains as a catalyst. Oxygen atoms arriving on the dust are released into the gas phase under the form of OH and H2O. The efficiencies of this conversion due to the chemistry occurring on dust are of order 30 percent for oxygen converted into OH and 60 percent for oxygen converted into H_2O between T_dust=15-40 K. At higher temperatures, the efficiencies rapidly decline. When the gas is mostly atomic, molecule formation on dust is dominant over the gas-phase route, which is then quenched by the low H2 abundance. Here, it is possible to enhance the warm (T> 200 K) water abundance by an order of magnitude in X-ray exposed environments. This helps to explain the observed bright water lines in nearby and high-redshift ULIRGs and Quasars.

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arXiv2011

Star formation near an obscured AGN: Variations in the initial mass function

The conditions that affect the formation of stars in radiatively and mechanically active environments are quite different than the conditions that apply to our local interstellar neighborhood. In such galactic environments, a variety of feedback processes can play a significant role in shaping the initial mass function (IMF). Here, we present a numerical study on the effects of an accreting black hole and the influence of nearby massive stars to a collapsing, 800 M_sun, molecular cloud at 10 pc distance from the black hole. We parametrize and study radiative feedback effects of hard X-rays emanating from the black hole broad line region, increased cosmic ray rates due to supernovae in starbursts, and strong UV radiation produced by nearby massive stars. We also investigate the importance of shear from the supermassive, 10^6-10^8 M_sun, black hole as the star-forming cloud orbits around it. We find that thermal pressure from X-rays compresses the cloud, which induces a high star formation rate early on, but reduces the overall star formation efficiency to about 7% due to gas depletion by evaporation. We see that the turn-over mass of the IMF increases up to a factor of 2.3, M_turn = 1-1.5 M_sun, for the model with the highest X-ray flux (160 erg s^-1 cm^-2), while the high-mass slope of the IMF becomes Gamma > -1. This results in more high mass stars and a non-Salpeter IMF. Cosmic rays penetrate deeply into the cloud and increase the gas temperature (50-200 K), which leads to a reduced formation efficiency of low mass stars. High cosmic ray rates increase the average mass of stars, thereby shifting the turn-over mass to higher values, i.e., up to several solar masses. Due to this process, the onset of star formation is also delayed. We conclude that the IMF inside active galaxies is different than the one obtained from local environments.

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arXiv2011

Interstellar ices as witnesses of star formation: selective deuteration of water and organic molecules unveiled

Observations of star forming environments revealed that the abundances of some deuterated interstellar molecules are markedly larger than the cosmic D/H ratio of 10-5. Possible reasons for this pointed to grain surface chemistry. How- ever, organic molecules and water, which are both ice constituents, do not enjoy the same deuteration. For example, deuterated formaldehyde is very abundant in comets and star forming regions, while deuterated water rarely is. In this article, we explain this selective deuteration by following the formation of ices (using the rate equation method) in translucent clouds, as well as their evolu- tion as the cloud collapses to form a star. Ices start with the deposition of gas phase CO and O onto dust grains. While reaction of oxygen with atoms (H or D) or molecules (H2) yields H2O (HDO), CO only reacts with atoms (H and D) to form H2CO (HDCO, D2CO). As a result, the deuteration of formaldehyde is sensitive to the gas D/H ratio as the cloud undergoes gravitational collapse, while the deuteration of water strongly depends on the dust temperature at the time of ice formation. These results reproduce well the deuterium fractionation of formaldehyde observed in comets and star forming regions and can explain the wide spread of deuterium fractionation of water observed in these environments.

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arXiv2011

Diffuse interstellar bands in Upper Scorpius: Probing variations in the DIB spectrum due to changing environmental conditions

We study the effects of local environmental conditions affecting the diffuse interstellar band (DIB) carriers within the Upper Scorpius subgroup of the Sco OB2 association. We obtained optical spectra with FEROS, and measured the equivalent widths of five DIBs (at 5780, 5797, 6196, 6379, and 6613 Angstrom) as well as those of absorption lines of di-atomic molecules (CH, CH+, CN) and atoms (KI, CaI) towards 89 targets in the direction of Upper Scorpius. We construct a simple radiative transfer and chemical network model of the diffuse interstellar medium (ISM) sheet in front of Upp Sco to infer the effective radiation field. Both the interstellar radiation field strength, I_UV, and the molecular hydrogen fraction, f_H2, have been derived for 55 sightlines probing the Upp Sco ISM. We discuss the relations between DIB strengths, CH and CH+ line strengths, E(B-V), I_UV, and f_H2. The ratio between the 5780 and 5797 DIBs reveals a (spatial) dependence on the local environment in terms of cloud density and exposure to the interstellar radiation field, reflecting the molecular nature of these DIB carriers.

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arXiv2011

When sticking influences H2 formation

Aims. Interstellar dust grains, because of their catalytic properties, are crucial to the formation of H2, the most abundant molecule in the Universe. The formation of molecular hydrogen strongly depends on the ability of H atoms to stick on dust grains. In this study we determine the sticking coefficient of H atoms chemisorbed on graphitic surfaces, and estimate its impact on the forma- tion of H2. Methods. The sticking probability of H atoms chemisorbed onto graphitic surfaces is obtained using a mixed classical-quantum dynamics method. In this, the H atom is treated quantum- mechanically and the vibrational modes of the surface are treated classically. The implications of sticking for the formation of H2 are addressed by using Kinetic Monte Carlo simulations that follow how atoms stick, move and associate with each other on dust surfaces of different temper- ature. Results. In our model, molecular hydrogen forms very efficiently for dust temperatures lower than 15 K through the involvement of physisorbed H atoms. At dust temperatures higher than 15 K and gas temperatures lower than 2000 K, H2 formation differs strongly if the H atoms com- ing from the gas phase have to cross a square barrier (usually considered in previous studies) or a barrier obtained by DFT calculations to become chemisorbed. The product of sticking times efficiency can be increased by many orders of magnitude when realistic barriers are considered. If graphite phonons are taken into account in the dynamics calculations, then H atoms stick better on the surface at high energies, but the overall H2 formation efficiency is only slightly affected. Our results suggest that H2 formation can proceed efficiently in photon dominated regions, X-ray dominated regions, hot cores and in the early Universe when the first dust is available.

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arXiv2011

The deeply obscured AGN of NGC4945 I. Spitzer-IRS maps of [Ne V], [Ne II], H2 0-0 S(1), S(2), and other tracers

The nearly edge-on galaxy NGC4945 is one of the closest galaxies where an AGN and starburst coexist, and is one of the brightest sources at 100 keV. Near and mid-infrared spectroscopy have shown very strong obscuration of its central region, rivaled only in strength by some of the most deeply obscured ULIRGs. We aim to determine the spatial distribution of ISM features in the central 426x426 pc^2 of NGC4945. We map the central region of NGC4945 in three Spitzer-IRS modules (SH, SL and LL). We produce maps of the flux distribution of the starburst tracers [Ne II], [Ne III], [S III] and [S IV] at 12.81, 15.56, 18.71 and 10.51 mum, respectively, and a map of the AGN narrow-line region tracer [Ne V] at 14.32 mum. We also mapped the S(1), S(2) and S(3) pure rotational lines of H2, which trace the distribution of warm molecular hydrogen. We obtained an extinction map (A_V) based on the apparent strength of the 9.7 mum silicate absorption feature. Our A_V map traces the contours of the starburst ring but the highest extinction (A_V(9.85 mum)~60) is found at the nucleus. Within the uncertainty of the astrometry all emission lines are found to peak on the nucleus, except for the warm molecular hydrogen emission which shows a maximum 60-100 pc NW of the nucleus. We favour a scenario in which the lower H2 0-0 S(1) and S(2) rotational lines originate mainly from an unobscured extra-nuclear component associated with the super-wind cone observed in the HST NICMOS map of the H2 1-0 S(1) vibrational line. For the [Ne V] emission we infer an attenuation of a factor 12-160 (A_V=55-112) based on a comparison of the ratio of our [Ne V] flux and the absorption-corrected 14-195 keV Swift-BAT flux to the average [Ne V]/BAT ratio for Seyfert 1 nuclei. The high attenuation indicates that [Ne V] and [O IV] cannot be used as extinction-free tracers of AGN power in galaxies with deeply buried nuclei.

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arXiv2011

Lyman alpha emission from the first galaxies: Implications of UV backgrounds and the formation of molecules

The Lyman alpha line is a robust tracer of high redshift galaxies. We present estimates of Lyman alpha emission from a protogalactic halo illuminated by UV background radiation fields with various intensities. For this purpose, we performed cosmological hydrodynamics simulations with the adaptive mesh refinement code FLASH, including a detailed network for primordial chemistry,comprising the formation of primordial molecules, a multi-level model for the hydrogen atom as well as the photo-ionization and photo-dissociation processes in a UV background. We find that the presence of a background radiation field J_21 excites the emission of Lyman alpha photons, increasing the Lyman alpha luminosity up to two orders of magnitude. For a halo of \sim 10^10 M_sun, we find that a maximum flux of 5 \times 10^-15 erg cm^-2 s^-1 is obtained for J21 \times f_esc = 0.1, where f_esc is the escape fraction of the ionizing radiation. Depending on the environmental conditions, the flux may vary by three orders of magnitude. For J_21 \times f_esc > 0.1 the Lyman alpha luminosity decreases as the atomic hydrogen abundance becomes rather small. The fluxes derived here can be probed using Subaru and the upcoming James Webb Space Telescope. The emission of Lyman alpha photons is extended and comes from the envelope of the halo rather than its core. In the center of the halo, line trapping becomes effective above columns of 10^22 cm^-2 and suppresses the emission of Lyman alpha. In addition, cooling by primordial molecules may decrease the gas temperature in the central region, which further reduces Lyman alpha emission. In the central core, H_2 is photo-dissociated for a background flux of J_21 \geq 1000. For weaker radiation fields, i.e. J_21 < 0.1, H_2 and HD cooling are particularly strong in the center of the halo, leading to gas temperatures as low as \sim 100 K.

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arXiv2011

Lyman alpha emission from the first galaxies: Signatures of accretion and infall in the presence of line trapping

The formation of the first galaxies is accompanied by large accretion flows and virialization shocks, during which the gas is shock-heated to temperatures of $\sim10^4$ K, leading to potentially strong fluxes in the Lyman alpha line. Indeed, a number of Lyman alpha blobs has been detected at high redshift. In this letter, we explore the origin of such Lyman alpha emission using cosmological hydrodynamical simulations that include a detailed model of atomic hydrogen as a multi-level atom and the effects of line trapping with the adaptive mesh refinement code FLASH. We see that baryons fall into the center of a halo through cold streams of gas, giving rise to a Lyman alpha luminosity of at least $\rm 10^{44} erg s^{-1}$ at $\rm z=4.7$, similar to observed Lyman alpha blobs. We find that a Lyman alpha flux of $\rm 5.0\times 10^{-17} erg cm^{-2} s^{-1}$ emerges from the envelope of the halo rather than its center, where the photons are efficiently trapped. Such emission can be probed in detail with the upcoming James Webb Space Telescope (JWST) and will constitute an important probe of gas infall and accretion.

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arXiv2011

The JCMT Spectral Legacy Survey: physical structure of the molecular envelope of the high-mass protostar AFGL2591

The understanding of the formation process of massive stars (>8 Msun) is limited, due to theoretical complications and observational challenges. We investigate the physical structure of the large-scale (~10^4-10^5 AU) molecular envelope of the high-mass protostar AFGL2591 using spectral imaging in the 330-373 GHz regime from the JCMT Spectral Legacy Survey. Out of ~160 spectral features, this paper uses the 35 that are spatially resolved. The observed spatial distributions of a selection of six species are compared with radiative transfer models based on a static spherically symmetric structure, a dynamic spherical structure, and a static flattened structure. The maps of CO and its isotopic variations exhibit elongated geometries on scales of ~100", and smaller scale substructure is found in maps of N2H+, o-H2CO, CS, SO2, CCH, and methanol lines. A velocity gradient is apparent in maps of all molecular lines presented here, except SO, SO2, and H2CO. We find two emission peaks in warm (Eup~200K) methanol separated by 12", indicative of a secondary heating source in the envelope. The spherical models are able to explain the distribution of emission for the optically thin H13CO+ and C34S, but not for the optically thick HCN, HCO+, and CS, nor for the optically thin C17O. The introduction of velocity structure mitigates the optical depth effects, but does not fully explain the observations, especially in the spectral dimension. A static flattened envelope viewed at a small inclination angle does slightly better. We conclude that a geometry of the envelope other than an isotropic static sphere is needed to circumvent line optical depth effects. We propose that this could be achieved in envelope models with an outflow cavity and/or inhomogeneous structure at scales smaller than ~10^4 AU. The picture of inhomogeneity is supported by observed substructure in at least six species.

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arXiv2010

X-ray impact on the protoplanetary disks around T Tauri stars

Context: T Tauri stars have X-ray luminosities ranging from L_X = 10^28-10^32 erg/s. These luminosities are similar to UV luminosities (L_UV 10^30-10^31 erg/s) and therefore X-rays are expected to affect the physics and chemistry of the upper layers of their surrounding protoplanetary disks. Aim: The effects and importance of X-rays on the chemical and hydrostatic structure of protoplanetary disks are investigated, species tracing X-ray irradiation (for L_X >= 10^29 erg/s) are identified and predictions for [OI], [CII] and [NII] fine structure line fluxes are provided. Methods: We have implemented X-ray physics and chemistry into the chemo-physical disk code ProDiMo. We include Coulomb heating and H2 ionization as heating processes and primary and secondary ionization due to X-rays in the chemistry. Results: X-rays heat up the gas causing it to expand in the optically thin surface layers. Neutral molecular species are not much affected in their abundance and spatial distribution, but charged species such as N+, OH+, H2O+ and H3O+ show enhanced abundances in the disk surface. Conclusions: Coulomb heating by X-rays changes the vertical structure of the disk, yielding temperatures of ~ 8000 K out to distances of 50 AU. The chemical structure is altered by the high electron abundance in the gas in the disk surface, causing an efficient ion-molecule chemistry. The products of this, OH+, H2O+ and H3O+, are of great interest for observations of low-mass young stellar objects with the Herschel Space Observatory. [OI] (at 63 and 145 mic) and [CII] (at 158 mic) fine structure emission are only affected for L_X > 10^30 erg/s.

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arXiv2010

Star Formation in Extreme Environments: The Effects of Cosmic Rays and Mechanical Heating

Context: Molecular data of extreme environments, such as Arp 220, but also NGC 253, show evidence for extremely high cosmic ray (CR) rates (10^3-10^4 * Milky Way) and mechanical heating from supernova driven turbulence. Aims: The consequences of high CR rates and mechanical heating on the chemistry in clouds are explored. Methods: PDR model predictions are made for low, n=10^3, and high, n=10^5.5 cm^-3, density clouds using well-tested chemistry and radiation transfer codes. Column densities of relevant species are discussed, and special attention is given to water related species. Fluxes are shown for fine-structure lines of O, C+, C, and N+, and molecular lines of CO, HCN, HNC, and HCO+. A comparison is made to an X-ray dominated region model. Results: Fine-structure lines of [CII], [CI], and [OI] are remarkably similar for different mechanical heating and CR rates, when already exposed to large amounts of UV. HCN and H2O abundances are boosted for very high mechanical heating rates, while ionized species are relatively unaffected. OH+ and H2O+ are enhanced for very high CR rates zeta > 5 * 10^-14 s^-1. A combination of OH+, OH, H2O+, H2O, and H3O+ trace the CR rates, and are able to distinguish between enhanced cosmic rays and X-rays.

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arXiv2010

The Impact of Lyman alpha Trapping on the Formation of Primordial Objects

Numerous cosmological simulations have been performed to study the formation of the first objects. We present the results of high resolution 3-D cosmological simulations of primordial objects formation using the adaptive mesh refinement code FLASH by including in an approximate manner the radiative transfer effects of Lyman alpha photons. We compare the results of a Lyman alpha trapping case inside gas clouds with atomic and molecular hydrogen cooling cases.The principal objective of this research is to follow the collapse of a zero metallicity halo with an effective equation of state (that accounts for the trapping) and to explore the fate of a halo in each of the three cases, specifically, the impact of thermodynamics on fragmentation of halos.Our results show that in the case of Lyman alpha trapping, fragmentation is halted and a massive object is formed at the center of a halo. The temperature of the gas remains well above $10^{4}$ K and the halo is not able to fragment to stellar masses. In the atomic cooling case, gas collapses into one or two massive clumps in contrast to the Lyman alpha trapping case. For the molecular hydrogen cooling case, gas cools efficiently and fragments.The formation of massive primordial objects is thus strongly dependent on the thermodynamics of the gas. A salient feature of our results is that for the formation of massive objects, e.g. intermediate mass black holes, feedback effects are not required to suppress $H_{2}$ cooling, as molecular hydrogen is collisionally dissociated at temperatures higher than $10^{4}$ K as a consequence of Lyman alpha trapping.

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arXiv2010

The impact of X-rays on molecular cloud fragmentation and the IMF

Star formation is regulated through a variety of feedback processes. In this study, we treat feedback by X-rays and discuss its implications. Our aim is to investigate whether star formation is significantly affected when a star forming cloud resides in the vicinity of a strong X-ray source. We perform an Eulerian grid simulation with embedded Lagrangian sink particles of a collapsing molecular cloud near a massive, 10^7 M_o black hole. The chemical and thermal changes caused by radiation are incorporated into the FLASH code. When there is strong X-ray feedback the star forming cloud fragments into larger clumps whereby fewer but more massive protostellar cores are formed. Competitive accretion has a strong impact on the mass function and a near-flat, non-Salpeter IMF results.

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arXiv2010

Water formation on bare grains: When the chemistry on dust impacts interstellar gas

Context. Water together with O2 are important gas phase ingredients to cool dense gas in order to form stars. On dust grains, H2 O is an important constituent of the icy mantle in which a complex chemistry is taking place, as revealed by hot core observations. The formation of water can occur on dust grain surfaces, and can impact gas phase composition. Aims. The formation of molecules such as OH, H2 O, HO2, H2 O2, as well as their deuterated forms and O2 and O3 is studied in order to assess how the chemistry varies in different astrophysical environments, and how the gas phase is affected by grain surface chemistry. Methods. We use Monte Carlo simulations to follow the formation of molecules on bare grains as well as the fraction of molecules released into the gas phase. We consider a surface reaction network, based on gas phase reactions, as well as UV photo-dissociation of the chemical species. Results. We show that grain surface chemistry has a strong impact on gas phase chemistry, and that this chemistry is very different for different dust grain temperatures. Low temperatures favor hydrogenation, while higher temperatures favor oxygenation. Also, UV photons dissociate the molecules on the surface, that can reform subsequently. The formation-destruction cycle increases the amount of species released into the gas phase. We also determine the time scales to form ices in diffuse and dense clouds, and show that ices are formed only in shielded environments, as supported by observations.

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arXiv2010

Accretion among preplanetary bodies: the many faces of runaway growth

(abridged) When preplanetary bodies reach proportions of ~1 km or larger in size, their accretion rate is enhanced due to gravitational focusing (GF). We have developed a new numerical model to calculate the collisional evolution of the gravitationally-enhanced growth stage. We validate our approach against existing N-body and statistical codes. Using the numerical model, we explore the characteristics of the runaway growth and the oligarchic growth accretion phases starting from an initial population of single planetesimal radius R_0. In models where the initial random velocity dispersion (as derived from their eccentricity) starts out below the escape speed of the planetesimal bodies, the system experiences runaway growth. We find that during the runaway growth phase the size distribution remains continuous but evolves into a power-law at the high mass end, consistent with previous studies. Furthermore, we find that the largest body accretes from all mass bins; a simple two component approximation is inapplicable during this stage. However, with growth the runaway body stirs up the random motions of the planetesimal population from which it is accreting. Ultimately, this feedback stops the fast growth and the system passes into oligarchy, where competitor bodies from neighboring zones catch up in terms of mass. Compared to previous estimates, we find that the system leaves the runaway growth phase at a somewhat larger radius. Furthermore, we assess the relevance of small, single-size fragments on the growth process. In classical models, where the initial velocity dispersion of bodies is small, these do not play a critical role during the runaway growth; however, in models that are characterized by large initial relative velocities due to external stirring of their random motions, a situation can emerge where fragments dominate the accretion.

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