arXiv subjects

R. E. Pudritz

Publications and source records attributed to R. E. Pudritz.

At least 19 recordsLinked to original sources

arXiv2026

The CepA disk-outflow system at <=0.2'' or <=100au resolution

Context: Although there has been significant progress, the physical properties and potential fragmentation of accretion disks around high-mass protostars remain poorly constrained. Aims: We characterize at high angular resolution one of the most nearby (~700pc) high-mass accretion disk candidates CepA HW2. Methods: Using the new long baseline array configuration (~1700m) of the Northern Extended Millimeter Array (NOEMA), we study CepA HW2 with a resolution of <=0.2'' or <=100au at 1.3mm in dust continuum and spectral line emission. Results: The mm continuum emission resolves the central disk candidate into several sub-structures. Conducting a Toomre Q stability analysis based on CH_3CN and continuum data, and a comparison to 3D radiation hydrodynamic simulations shows that the data are consistent with an almost edge-on disk where the observed sub-structures may represent fragments within the disk. The CO and SiO spectral line data confirm a second bipolar outflow (in addition to the well-known jet) emanating from the central peak position. This indicates that this central peak should host at least a binary if not even a higher order multiple system. The usually assumed dense gas tracer CH_3CN shows also contributions from the outflows which complicates further kinematic analysis of the disk. Conclusions: The high-resolution outflow-disk data of CepA reveal a multiply fragmented disk that drives several outflows. These observations enforce the picture of high-mass star formation where multiplicity and fragmentation can happen on the smallest spatial scales related to the inner accretion disks.

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arXiv2026

Protostellar Outflows at the EarliesT Stages (POETS). IX. Magnetohydrodynamic disk winds traced by SO and SO$_2$ in luminous protostars

We investigate two massive young stellar objects (YSOs), IRAS21078+5211 and G035.02+0.35, where evidence for magnetohydrodynamic (MHD) disk winds (DWs) has been obtained at scales of 10-100 au through measurements of the 22GHz water maser velocity distribution within the Protostellar Outflows at the EarliesT Stages (POETS) survey. We employ IRAM Northern Extended Millimeter Array and archival Atacama Large Millimeter Array observations of IRAS21078+5211 and G035.02+0.35, respectively, to study kinematics and physical conditions of the corresponding protostellar winds on scales of 100-1000 au using the same molecular tracers. In IRAS21078+5211, the emissions of several molecules, particularly SO, SO2, CH3CN and CH3OH, are distributed along the axis of the radio jet, and present a LSR velocity (Vlsr) gradient transversal to the jet axis. Position-velocity (PV) plots of the SO lines show patterns consistent with Keplerian rotation. The SO2 emission comes from high velocity gas flowing close to the jet axis, while CH3CN and CH3OH present larger radial extension than the S-bearing species. In G035.02+0.35, the same molecules are instead distributed along the major axis of the rotating disk, and their Vlsr gradients consistently trace the disk rotation. The corresponding PV plots present Keplerian profiles. SO is the only molecular species whose emission extends well outside the disk. In both YSOs, the spatial and velocity distributions of SO are consistent with a rotating wind magneto-centrifugally launched from the YSO disk. The comparison with models of molecule formation and excitation in shocks indicates that the different radial extension of the molecular species observed in the protostellar wind of IRAS21078+5211, as well as the lack of molecules, except SO, in the G035.02+0.35's wind, can be explained in terms of a radially extended MHD DW, rather than a compact X-wind.

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arXiv2025

From theory to observation: understanding filamentary flows in high-mass star-forming clusters

Here we use data from multi-scale galactic MHD simulations to observe filaments and star forming clumps on 10's of pc scales and investigate flow rate relationships along, and onto filaments as well as flows towards the clumps. Using the FilFinderPPV identification technique, we identify the prominent filamentary structures in each data cube. Each filament and its corresponding clump are analysed by calculating flow rates along each filament towards the clump, onto each filament from increasing distances, and radially around each clump. This analysis is conducted for two cubes, one feedback dominated region, and one with less feedback. Looking at the face-on inclination of the simulations (0 degrees), we observe different trends depending on the environmental conditions (more or less feedback). The median flow rate in the region with more feedback is 8.9$\times$10$^{-5}$ M$_{sun}\mathrm{yr}^{-1}$ and we see that flow rates along the filaments toward the clumps generally decrease in these regions. In the region with less feedback we have a median flow rate of 2.9$\times$10$^{-4}$ M$_{sun}\mathrm{yr}^{-1}$ and when looking along the filaments here we see the values either increase or remain constant. We find that the flow rates from the environments onto the primary filaments are of an order of magnitude sufficient to sustain the flow rates along these filaments. When discussing the effects of galactic and filamentary inclination, we also observe that viewing the filaments from different galactic inclinations can reveal the presence of feeder structures (smaller filamentary structures aiding in the flow of material). The method used to estimate these flow rates, which has been previously applied to observational data, produced results consistent with those obtained from the simulations themselves, providing high confidence in the flow rate calculation method.

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arXiv2025

On the relation between magnetic field strength and gas density in the interstellar medium: A multiscale analysis

The magnetic field strength to gas density relation in the interstellar medium is of fundamental importance. We present and compare Bayesian analyses of the B-n relation for two comprehensive observational data sets: a Zeeman data set and 700 observations using the Davis-Chandrasekhar-Fermi (DCF) method. Using a hierarchical Bayesian analysis we present a general, multi-scale broken power-law relation, $B=B_0(n/n_0)^α$ , with $α=α_1$ for $n n_0$, and with $B_0$ the field strength at $n_0$. For the Zeeman data we find: $α_1={0.15^{+0.06}_{-0.09}}$ for diffuse gas and $α_2 = {0.53^{+0.09}_{-0.07}}$ for dense gas with $n_0 = 4.00^{+12.7}_{-2.90} \times 10^3$ cm$^{-3}$. For the DCF data we find: $α_1={0.26^{+0.15}_{-0.15}}$ and $α_2={0.77_{-0.15}^{+0.14}}$, with $n_0=13.9^{+10.1}_{-7.30} \times 10^4$ cm$^{-3}$, where the uncertainties give 68\% credible intervals. We perform a similar analysis on nineteen numerical magnetohydrodynamic simulations covering a wide range of physical conditions from protostellar disks to dwarf and Milky Way-like galaxies, completed with the AREPO, Flash, Pencil, and Ramses codes. The resulting exponents depend on several physical factors such as dynamo effects and their time scales, turbulence, and initial seed field strength. \textcolor{red}{We find that the dwarf and Milky Way-like galaxy simulations produce results closest to the observations.

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arXiv2023

Kinematics and stability of high-mass protostellar disk candidates at sub-arcsecond resolution -- Insights from the IRAM NOEMA large program CORE

The fragmentation mode of high-mass molecular clumps and the accretion processes that form the most massive stars ($M\gtrsim 8M_\odot$) are still not well understood. To this end, we have undertaken a large observational program (CORE) making use of interferometric observations from the Northern Extended Millimetre Array (NOEMA) for a sample of 20 luminous ($L>10^4L_\odot$) protostellar objects in the 1.37 mm wavelength regime in both continuum and line emission, reaching $\sim$0.4" resolution (800 au at 2 kpc). Using the dense gas tracer CH$_3$CN, we find velocity gradients across 13 cores perpendicular to the directions of bipolar molecular outflows, making them excellent disk candidates. Specific angular momentum ($j$) radial profiles are on average $\sim10^{-3}$ km /s pc and follow $j \propto r^{1.7}$, consistent with a poorly resolved rotating and infalling envelope/disk model. Fitting the velocity profiles with a Keplerian model, we find protostellar masses in the range of $\sim 10-25$ $M_\odot$. Modelling the level population of CH$_3$CN lines, we present temperature maps and find median gas temperatures in the range $70-210$ K. We create Toomre $Q$ maps to study the stability of the disks and find almost all (11 of 13) disk candidates to be prone to fragmentation due to gravitational instabilities at the scales probed by our observations. In particular, disks with masses greater than $\sim10-20\%$ of the mass of their host (proto)stars are Toomre unstable, and more luminous protostellar objects tend to have disks that are more massive and hence more prone to fragmentation. Our finings show that most disks around high-mass protostars are prone to disk fragmentation early in their formation due to their high disk to stellar mass ratio. This impacts the accretion evolution of high-mass protostars which will have significant implications for the formation of the most massive stars.

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arXiv2021

Clustered star formation at early evolutionary stages. Physical and chemical analysis of the young star-forming regions ISOSS J22478+6357 and ISOSS J23053+5953

We aim to characterize the physical and chemical properties of fragmented cores during the earliest evolutionary stages in the very young star-forming regions ISOSS J22478+6357 and ISOSS J23053+5953. NOEMA 1.3 mm data are used in combination with archival mid- and far-infrared observations to construct and fit the SEDs of individual fragmented cores. The radial density profiles are inferred from the 1.3 mm continuum visibility profiles and the radial temperature profiles are estimated from H2CO rotation temperature maps. Molecular column densities are derived with the line fitting tool XCLASS. The physical and chemical properties are combined by applying the physical-chemical model MUSCLE in order to constrain the chemical timescales of a few line-rich cores. The morphology and spatial correlations of the molecular emission are analyzed using the HOG method. The mid-infrared data show that both regions contain a cluster of young stellar objects. Bipolar molecular outflows are observed in the CO 2-1 transition toward the strong mm cores indicating protostellar activity. We find strong molecular emission of SO, SiO, H2CO, and CH3OH in locations which are not associated with the mm cores. These shocked knots can be either associated with the bipolar outflows or, in the case of ISOSS J23053+5953, with a colliding flow that creates a large shocked region between the mm cores. The mean chemical timescale of the cores is lower (20 000 yr) compared to that of the sources of the more evolved CORE sample (60 000 yr). With the HOG method, we find that the spatial emission of species tracing the extended emission and of shock-tracing molecules are well correlated within transitions of these groups.

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arXiv2021

Disk fragmentation in high-mass star formation. High-resolution observations towards AFGL 2591-VLA 3

Increasing evidence suggests that, similar to their low-mass counterparts, high-mass stars form through a disk-mediated accretion process. At the same time, formation of high-mass stars still necessitates high accretion rates, and hence, high gas densities, which in turn can cause disks to become unstable against gravitational fragmentation. We study the kinematics and fragmentation of the disk around the high-mass star forming region AFGL 2591-VLA 3 which was hypothesized to be fragmenting based on the observations that show multiple outflow directions. We use a new set of high-resolution (0.19 arcsec) IRAM/NOEMA observations at 843 micron towards VLA 3 which allow us to resolve its disk, characterize the fragmentation, and study its kinematics. In addition to the 843 micron continuum emission, our spectral setup targets warm dense gas and outflow tracers such as HCN, HC$_3$N and SO$_2$, as well as vibrationally excited HCN lines. The high resolution continuum and line emission maps reveal multiple fragments with subsolar masses within the inner 1000 AU of VLA 3. Furthermore, the velocity field of the inner disk observed at 843 micron shows a similar behavior to that of the larger scale velocity field studied in the CORE project at 1.37 mm. We present the first observational evidence for disk fragmentation towards AFGL 2591-VLA 3, a source that was thought to be a single high-mass core. While the fragments themselves are low-mass, the rotation of the disk is dominated by the protostar with a mass of 10.3$\pm 1.8~M_{\odot}$. These data also show that NOEMA Band 4 can obtain the highest currently achievable spatial resolution at (sub-)mm wavelengths in observations of strong northern sources.

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arXiv2021

Multi-scale view of star formation in IRAS 21078+5211: From clump fragmentation to disk wind

In the massive star-forming region IRAS 21078+5211, a highly fragmented cluster (0.1~pc in size) of molecular cores is observed, located at the density peak of an elongated (1~pc in size) molecular cloud. A small (1~km/s per 0.1~pc) LSR velocity (Vlsr) gradient is detected across the axis of the molecular cloud. Assuming we are observing a mass flow from the harboring cloud to the cluster, we derive a mass infall rate of about 10^{-4}~M_{sun}~yr^{-1}. The most massive cores (labeled 1, 2, and 3) are found at the center of the cluster, and these are the only ones that present a signature of protostellar activity in terms of emission from high-excitation molecular lines or a molecular outflow. We reveal an extended (size about 0.1~pc), bipolar collimated molecular outflow emerging from core 1. We believe this is powered by a (previously discovered) compact (size <= 1000~au) radio jet, ejected by a YSO embedded in core 1 (named YSO-1), since the molecular outflow and the radio jet are almost parallel and have a comparable momentum rate. By means of high-excitation lines, we find a large (14~km/s over 500~au) Vlsr gradient at the position of YSO-1, oriented approximately perpendicular to the radio jet. Assuming this is an edge-on, rotating disk and fitting a Keplerian rotation pattern, we determine the YSO-1 mass to be 5.6+/-2.0~M_{sun}. The water masers (previously observed with VLBI) emerge within 100-300~au from YSO-1 and are unique tracers of the jet kinematics. Their three-dimensional (3D) velocity pattern reveals that the gas flows along, and rotates about, the jet axis. We show that the 3D maser velocities are fully consistent with the magneto-centrifugal disk-wind models predicting a cylindrical rotating jet. Under this hypothesis, we determine the jet radius to be about 16~au and the corresponding launching radius and terminal velocity to be about 2.2~au and 200~km/s, respectively.

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arXiv2019

IRAS23385+6053: An embedded massive cluster in the making

This study is part of the project ``CORE'', an IRAM/NOEMA large program consisting of observations of the millimeter continuum and molecular line emission towards 20 selected high-mass star forming regions. We focus on IRAS23385+6053, which is believed to be the least evolved source of the CORE sample. The observations were performed at ~1.4 mm and employed three configurations of NOEMA and additional single-dish maps, merged with the interferometric data to recover the extended emission. Our correlator setup covered a number of lines from well-known hot core tracers and a few outflow tracers. The angular (~0.45"$-$0.9") and spectral (0.5 km/s) resolutions were sufficient to resolve the clump in IRAS23385+6053 and investigate the existence of large-scale motions due to rotation, infall, or expansion. We find that the clump splits into six distinct cores when observed at sub-arcsecond resolution. These are identified through their 1.4 mm continuum and molecular line emission. We produce maps of the velocity, line width, and rotational temperature from the methanol and methyl cyanide lines, which allow us to investigate the cores and reveal a velocity and temperature gradient in the most massive core. We also find evidence of a bipolar outflow, possibly powered by a low-mass star. We present the tentative detection of a circumstellar self-gravitating disk lying in the most massive core and powering a large-scale outflow previously known in the literature. In our scenario, the star powering the flow is responsible for most of the luminosity of IRAS23385+6053 (~$3000~L_\odot$). The other cores, albeit with masses below the corresponding virial masses, appear to be accreting material from their molecular surroundings and are possibly collapsing or on the verge of collapse. We conclude that we are observing a sample of star-forming cores that is bound to turn into a cluster of massive stars.

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arXiv2014

Accretion and magnetic field morphology around Class 0 stage protostellar discs

We analyse simulations of turbulent, magnetised molecular cloud cores focussing on the formation of Class 0 stage protostellar discs and the physical conditions in their surroundings. We show that for a wide range of initial conditions Keplerian discs are formed in the Class 0 stage already. In particular, we show that even subsonic turbulent motions reduce the magnetic braking efficiency sufficiently in order to allow rotationally supported discs to form. We therefore suggest that already during the Class 0 stage the fraction of Keplerian discs is significantly higher than 50%, consistent with recent observational trends but significantly higher than predictions based on simulations with misaligned magnetic fields, demonstrating the importance of turbulent motions for the formation of Keplerian discs. We show that the accretion of mass and angular momentum in the surroundings of protostellar discs occurs in a highly anisotropic manner, by means of a few narrow accretion channels. The magnetic field structure in the vicinity of the discs is highly disordered, revealing field reversals up to distances of 1000 AU. These findings demonstrate that as soon as even mild turbulent motions are included, the classical disc formation scenario of a coherently rotating environment and a well-ordered magnetic field breaks down. Hence, it is highly questionable to assess the magnetic braking efficiency based on non-turbulent collapse simulation. We strongly suggest that, in addition to the global magnetic field properties, the small-scale accretion flow and detailed magnetic field structure have to be considered in order to assess the likelihood of Keplerian discs to be present.

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arXiv2013

Turbulence-induced disc formation in strongly magnetised cloud cores

We present collapse simulations of strongly magnetised, turbulent molecular cloud cores with masses ranging from 2.6 to 1000 M_sun in order to study the influence of the initial conditions on the turbulence-induced disc formation mechanism proposed recently by Seifried et al. 2012. We find that Keplerian discs are formed in all cases independently of the core mass, the strength of turbulence, or the presence of global rotation. The discs appear within a few kyr after the formation of the protostar, are 50 - 150 AU in size, and have masses between 0.05 and a few 0.1 M_sun. During the formation of the discs the mass-to-flux ratio stays well below the critical value of 10 for Keplerian disc formation. Hence, flux-loss alone cannot explain the formation of Keplerian discs. The formation of rotationally supported discs at such early phases is rather due to the disordered magnetic field structure and due to turbulent motions in the surroundings of the discs, two effects lowering the classical magnetic braking efficiency. Binary systems occurring in the discs are mainly formed via the disc capturing mechanism rather than via disc fragmentation, which is largely suppressed by the presence of magnetic fields.

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arXiv2012

Disc formation in turbulent cloud cores: Circumventing the magnetic braking catastrophe

We present collapse simulations of strongly magnetised, 100 M_sun, turbulent cloud cores. Around the protostars formed during the collapse Keplerian discs with typical sizes of up to 100 AU build up in contrast to previous simulations neglecting turbulence. Analysing the condensations in which the discs form, we show that the magnetic flux loss is not sufficient to explain the build-up of Keplerian discs. The average magnetic field is strongly inclined to the disc which might reduce the magnetic braking efficiency. However, the main reason for the reduced magnetic braking efficiency is the highly disordered magnetic field in the surroundings of the discs. Furthermore, due to the lack of a coherently rotating structure in the turbulent environment of the disc no toroidal magnetic field necessary for angular momentum extraction can build up. Simultaneously the angular momentum inflow remains high due to local shear flows created by the turbulent motions. We suggest that the "magnetic braking catastrophe" is an artefact of the idealised non-turbulent initial conditions and that turbulence provides a natural mechanism to circumvent this problem.

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arXiv2012

Magnetic Fields in Astrophysical Jets: From Launch to Termination

Long-lived, stable jets are observed in a wide variety of systems, from protostars, through Galactic compact objects to active galactic nuclei (AGN). Magnetic fields play a central role in launching, accelerating, and collimating the jets through various media. The termination of jets in molecular clouds or the interstellar medium deposits enormous amounts of mechanical energy and momentum, and their interactions with the external medium, as well, in many cases, as the radiation processes by which they are observed, are intimately connected with the magnetic fields they carry. This review focuses on the properties and structures of magnetic fields in long-lived jets, from their launch from rotating magnetized young stars, black holes, and their accretion discs, to termination and beyond. We compare the results of theory, numerical simulations, and observations of these diverse systems and address similarities and differences between relativistic and non-relativistic jets in protostellar versus AGN systems. On the observational side, we focus primarily on jets driven by AGN because of the strong observational constraints on their magnetic field properties, and we discuss the links between the physics of these jets on all scales.

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arXiv2012

Disc formation in turbulent massive cores: Circumventing the magnetic braking catastrophe

We present collapse simulations of 100 M_{\sun}, turbulent cloud cores threaded by a strong magnetic field. During the initial collapse phase filaments are generated which fragment quickly and form several protostars. Around these protostars Keplerian discs with typical sizes of up to 100 AU build up in contrast to previous simulations neglecting turbulence. We examine three mechanisms potentially responsible for lowering the magnetic braking efficiency and therefore allowing for the formation of Keplerian discs. Analysing the condensations in which the discs form, we show that the build-up of Keplerian discs is neither caused by magnetic flux loss due to turbulent reconnection nor by the misalignment of the magnetic field and the angular momentum. It is rather a consequence of the turbulent surroundings of the disc which exhibit no coherent rotation structure while strong local shear flows carry large amounts of angular momentum. We suggest that the "magnetic braking catastrophe", i.e. the formation of sub-Keplerian discs only, is an artefact of the idealised non-turbulent initial conditions and that turbulence provides a natural mechanism to circumvent this problem.

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arXiv2012

Magnetic fields during the early stages of massive star formation - II. A generalised outflow criterion

Numerical simulations of outflows formed during the collapse of 100 M_sun cloud cores are presented. We derive a generalised criterion from MHD wind theory to analyse the launching mechanism of these outflows. The criterion is successfully applied to the whole outflow structure and cases with sub-Keplerian disc rotation. It allows us to decide whether an outflow is driven centrifugally or by the toroidal magnetic pressure. We show that quantities such as the magnetic field line inclination or the ratio of the toroidal to poloidal magnetic field alone are insufficient to determine the driving mechanism of outflows. By performing 12 runs we are able to study the influence of the initial conditions on the properties of outflows around massive protostars in detail. Our simulations reveal a strong effect of the magnetic field strength on the outflow morphology. In runs with weak fields or high rotational energies, well collimated, fast jets are observed whereas for strong fields poorly collimated, low-velocity outflows are found. We show that the occurrence of a fast jet is coupled to the existence of a Keplerian protostellar disc. Despite the very different morphologies all outflows are launched from the discs by centrifugal acceleration with the toroidal magnetic field increasingly contributing to the gas acceleration further away from the discs. The poor collimation of the outflows in runs with strong fields is a consequence of the weak hoop stresses. This in turn is caused by the slow build-up of a toroidal field due to sub-Keplerian disc rotation. The mass ejection/accretion ratios scatter around a mean of 0.3 in accordance with observational and analytical results. We suggest an evolutionary scenario for the earliest stage of massive star formation in which initially poorly collimated outflows develop which progressively get better collimated due to the generation of fast jets.

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arXiv2011

Magnetic fields during the early stages of massive star formation - I. Accretion and disk evolution

We present simulations of collapsing 100 M_\sun mass cores in the context of massive star formation. The effect of variable initial rotational and magnetic energies on the formation of massive stars is studied in detail. We focus on accretion rates and on the question under which conditions massive Keplerian disks can form in the very early evolutionary stage of massive protostars. For this purpose, we perform 12 simulations with different initial conditions extending over a wide range in parameter space. The equations of magnetohydrodynamics (MHD) are solved under the assumption of ideal MHD. We find that the formation of Keplerian disks in the very early stages is suppressed for a mass-to-flux ratio normalised to the critical value μbelow 10, in agreement with a series of low-mass star formation simulations. This is caused by very efficient magnetic braking resulting in a nearly instantaneous removal of angular momentum from the disk. For weak magnetic fields, corresponding to μ> 10, large-scale, centrifugally supported disks build up with radii exceeding 100 AU. A stability analysis reveals that the disks are supported against gravitationally induced perturbations by the magnetic field and tend to form single stars rather than multiple objects. We find protostellar accretion rates of the order of a few 10^-4 M_\sun yr^-1 which, considering the large range covered by the initial conditions, vary only by a factor of ~ 3 between the different simulations. We attribute this fact to two competing effects of magnetic fields. On the one hand, magnetic braking enhances accretion by removing angular momentum from the disk thus lowering the centrifugal support against gravity. On the other hand, the combined effect of magnetic pressure and magnetic tension counteracts gravity by exerting an outward directed force on the gas in the disk thus reducing the accretion onto the protostars.

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arXiv2009

Quark-Novae, cosmic reionization, and early r-process element production

We examine the case for Quark-Novae (QNe) as possible sources for the reionization and early metal enrichment of the universe. Quark-Novae are predicted to arise from the explosive collapse (and conversion) of sufficiently massive neutron stars into quark stars. A Quark-Nova (QN) can occur over a range of time scales following the supernova event. For QNe that arise days to weeks after the supernovae, we show that dual-shock that arises as the QN ejecta encounter the supernova ejecta can produce enough photons to reionize hydrogen in most of the Inter-Galactic medium (IGM) by z ~ 6. Such events can explain the large optical depth tau_e ~ 0.1 as measured by WMAP, if the clumping factor, C, of the material being ionized is smaller than 10. We suggest a way in which a normal initial mass function (IMF) for the oldest stars can be reconciled with a large optical depth as well as the mean metallicity of the early IGM post reionization. We find that QN also make a contribution to r-process element abundances for atomic numbers A > 130. We predict that the main cosmological signatures of Quark-Novae are the gamma-ray bursts that announce their birth. These will be clustered at redshifts in the range z ~ 7-8 in our model.

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arXiv2008

Simulating hydromagnetic processes in star formation: introducing ambipolar diffusion into an adaptive mesh refinement code

Given the importance of simulating hydromagnetic processes that impact star formation, we have earlier developed a 3D adaptive mesh approach that allows us to include hydromagnetic processes during the formation and evolution of cores, discs, and stars in observed regions of star formation. In this paper, we take the next step in this program - namely - to develop a modified version of the 3D adaptive mesh refinement (AMR) code FLASH in which the ambipolar diffusion of the magnetic field in poorly ionized molecular gas is implemented. We approach the problem using a single-fluid approximation to simplify numerical calculations. In this paper, we present a series of test cases including oblique isothermal and non--isothermal C-shocks. We also present a study of the quasi-static collapse of an initial uniform, self-gravitating, magnetized sphere that is initially supported by its magnetic field against collapse (i.e. magnetically subcritical). Applications to the collapse of a pre-stellar Bonnor-Ebert sphere are presented in a companion paper.

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