arXiv subjects

Shantanu Basu

Publications and source records attributed to Shantanu Basu.

At least 73 records · Page 4Linked to original sources

arXiv2015

The Luminosity of Population III Star Clusters

We analyze the time evolution of the luminosity of a cluster of Population III protostars formed in the early universe. We argue from the Jeans criterion that primordial gas can collapse to form a cluster of first stars that evolve relatively independently of one another (i.e., with negligible gravitational interaction). We model the collapse of individual protostellar clumps using 2+1D nonaxisymmetric numerical hydrodynamics simulations. Each collapse produces a protostar surrounded by a massive disk (i.e., $M_{\rm disk} / M_{*} \gtrsim 0.1$), whose evolution we follow for a further 30--40 kyr. Gravitational instabilities result in the fragmentation and the formation of gravitationally bound clumps within the disk. The accretion of these fragments by the host protostar produces accretion and luminosity bursts on the order of $10^6\,\LSun$. Within the cluster, we show that a simultaneity of such events across several protostellar cluster members can elevate the cluster luminosity to 5--10${\times}$ greater than expected, and that the cluster spends $\sim15\%$ of it's star-forming history at these levels. This enhanced luminosity effect is particularly enabled in clusters of modest size with $\simeq$ 10--20 members. In one such instance, we identify a confluence of burst events that raise the luminosity to nearly $1000{\times}$ greater than the cluster mean luminosity, resulting in $L > 10^8\,\LSun$. This phenomenon arises solely through the gravitational-instability--driven episodic fragmentation and accretion that characterizes this early stage of protostellar evolution.

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arXiv2015

The MLP Distribution: A Modified Lognormal Power-Law Model for the Stellar Initial Mass Function

This work explores the mathematical properties of a distribution introduced by Basu & Jones (2004), and applies it to model the stellar initial mass function (IMF). The distribution arises simply from an initial lognormal distribution, requiring that each object in it subsequently undergoes exponential growth but with an exponential distribution of growth lifetimes. This leads to a modified lognormal with a power-law tail (MLP) distribution, which can in fact be applied to a wide range of fields where distributions are observed to have a lognormal-like body and a power-law tail. We derive important properties of the MLP distribution, like the cumulative distribution, the mean, variance, arbitrary raw moments, and a random number generator. These analytic properties of the distribution can be used to facilitate application to modeling the IMF. We demonstrate how the MLP function provides an excellent fit to the IMF compiled by Chabrier (2005) and how this fit can be used to quickly identify quantities like the mean, median, and mode, as well as number and mass fractions in different mass intervals.

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arXiv2014

Kinematics in Partially Ionised Molecular Clouds: Implications for the Transition to Coherence

Bailey & Basu (2014) show analysis of density and mass-to-flux ratio maps for simulations with either an ionisation profile which takes into account photoionisation (step-like profile) or a cosmic ray only ionisation profile. We extend this study to analyse the effect of these ionisation profiles on velocity structures, kinematics, and synthetic spectra. Clump regions are found to occur at the convergence of two flows with a low velocity region and velocity direction transition occurring at the junction. Models with evident substructure show that core formation occurs on the periphery of these velocity valleys. Analysis of synthetic spectra reveals the presence of large non-thermal components within low-density gas, especially for models with the step-like ionisation profile. All cores show small, sub-thermal relative motions compared to background gas. Large deviations within this analysis are due to the line of sight intersecting low- and high-density regions across the velocity switch transition. Positive deviations correspond to a foreground core moving away from the observer while negative deviations correspond to a background core moving toward the observer. Comparison of velocities resulting from different ionisation profiles suggest that high ionisation fractions yield supersonic velocities, up to two times the sound speed, while regions with low ionisation fractions tend to be subsonic or mildly supersonic. This suggests that the transition to coherence within cores could be a transition between high and low ionisation fractions within the gas.

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arXiv2014

Induced Core Formation Time in Subcritical Magnetic Clouds by Large-Scale Trans-Alfvénic Flows

We clarify the mechanism of accelerated core formation by large-scale nonlinear flows in subcritical magnetic clouds by finding a semi-analytical formula for the core formation time and describing the physical processes that lead to them. Recent numerical simulations show that nonlinear flows induce rapid ambipolar diffusion that leads to localized supercritical regions that can collapse. Here, we employ non-ideal magnetohydrodynamic simulations including ambipolar diffusion for gravitationally stratified sheets threaded by vertical magnetic fields. One of the horizontal dimensions is eliminated, resulting in a simpler two-dimensional simulation that can clarify the basic process of accelerated core formation. A parameter study of simulations shows that the core formation time is inversely proportional to the square of the flow speed when the flow speed is greater than the Alfvén speed. We find a semi-analytical formula that explains this numerical result. The formula also predicts that the core formation time is about three times shorter than that with no turbulence, when the turbulent speed is comparable to the Alfvén speed.

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arXiv2013

Non-Ideal Magnetohydrodynamic Simulations of the Two-Stage Fragmentation Model for Cluster Formation

We model molecular cloud fragmentation with thin disk non-ideal magnetohydrodynamic simulations that include ambipolar diffusion and partial ionization that transitions from primarily ultraviolet dominated to cosmic ray dominated regimes. These simulations are used to determine the conditions required for star clusters to form through a two-stage fragmentation scenario. Recent linear analyses have shown that the fragmentation length and time scales can undergo a dramatic drop across the column density boundary that separates the ultraviolet and cosmic ray dominated ionization regimes. As found in earlier studies, the absence of an ionization drop and regular perturbations leads to a single-stage fragmentation on parsec scales in transcritical clouds, so that the nonlinear evolution yields the same fragment sizes as predicted by linear theory. However, we find that a combination of initial transcritical mass-to-flux ratio, evolution through a column density regime in which the ionization drop takes place, and regular small perturbations to the mass-to-flux ratio are sufficient to cause a second stage of fragmentation during the nonlinear evolution. Cores of size ~0.1 pc are formed within an initial fragment of ~ pc size. Regular perturbations to the mass-to-flux ratio also accelerate the onset of runaway collapse.

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arXiv2013

Feedback regulated star formation: II. dual constraints on the SFE and the age spread of stars in massive clusters

We show that the termination of the star formation process by winds from massive stars in protocluster forming clumps imposes dual constraints on the star formation efficiencies (SFEs) and stellar age spreads ($Δτ_{*}$) in stellar clusters. We have considered two main classes of clump models. One class of models in one in which the core formation efficiency (CFE) per unit time and as a consequence the star formation rate (SFR) is constant in time and another class of models in which the CFE per unit time, and as a consequence the SFR, increases with time. Models with an increasing mode of star formation yield shorter age spreads (a few 0.1 Myrs) and typically higher SFEs than models in which star formation is uniform in time. We find that the former models reproduce remarkably well the SFE$-Δτ_{*}$ values of starburst clusters such as NGC 3603 YC and Westerlund 1, while the latter describe better the star formation process in lower density environments such as in the Orion Nebula Cluster. We also show that the SFE and $Δτ_{*}$ of massive clusters are expected to be higher in low metallicity environments. This could be tested with future large extragalactic surveys of stellar clusters. We advocate that placing a stellar cluster on the SFE-$Δτ_{*}$ diagram is a powerful method to distinguish between different stellar clusters formation scenarios such as between generic gravitational instability of a gas cloud/clump or as the result of cloud-cloud collisions. It is also a very useful tool for testing star formation theories and numerical models versus the observations.

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arXiv2013

Long-Term Evolution of Decaying MHD Turbulence in the Multiphase ISM

Supersonic turbulence in the interstellar medium (ISM) is believed to decay rapidly within a flow crossing time irrespective of the degree of magnetization. However, this general consensus of decaying magnetohydrodynamic (MHD) turbulence relies on local isothermal simulations, which are unable to take into account the roles of global structures of magnetic fields and the ISM. Utilizing three-dimensional MHD simulations including interstellar cooling and heating, we investigate decaying MHD turbulence within cold neutral medium sheets embedded in warm neutral medium. Early evolution of turbulent kinetic energy is consistent with previous results for decaying compressible MHD turbulence characterized by rapid energy decay with a power-law form of $E\propto t^{-1}$ and by short decay time compared to a flow crossing time. If initial magnetic fields are strong and perpendicular to the sheet, however, long-term evolution of the kinetic energy shows that a significant amount of turbulent energy ($\sim 0.2E_0$) still remains even after ten flow crossing times for models with periodic boundary conditions. The decay rate is also greatly reduced as the field strength increases for such initial and boundary conditions, but not if the boundary conditions are that for a completely isolated sheet. We analyze velocity power spectra of the remaining turbulence to show that in-plane, incompressible motions parallel to the sheet dominate at later times.

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arXiv2013

Magnetic Fields and the Formation of Cores and Disks

We review recent results of non-ideal magnetohydrodynamic models for the fragmentation of molecular clouds and the collapse of cloud cores to form protostar-disk systems. Thin-disk models can elucidate many aspects of the physical problem and allow the calculation of large dynamic range of time and length scales.

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arXiv2013

The Burst Mode of Accretion in Primordial Protostars

We study the formation and long-term evolution of primordial protostellar disks harbored by first stars using numerical hydrodynamics simulations in the thin-disk limit. The initial conditions are specified by pre-stellar cores with distinct mass, angular momentum, and temperature. This allows us to probe several tens of thousand years of the disk's initial evolution, during which we observe multiple episodes of fragmentation leading to the formation of gravitationally bound gaseous clumps within spiral arms. These fragments are torqued inward due to gravitational interaction with the spiral arms on timescales of 10^3 - 10^4 yr and accreted onto the growing protostar, giving rise to accretion and luminosity bursts. The burst phenomenon is fueled by continuing accretion of material falling onto the disk from the collapsing parent core, which replenishes the mass lost by the disk due to accretion, and triggers repetitive episodes of disk fragmentation. We show that the burst phenomenon is expected to occur for a wide spectrum of initial conditions in primordial pre-stellar cores and speculate on how the intense luminosities (~10^7 solar luminosities) produced by this mechanism may have important consequences for the disk evolution and subsequent growth of the protostar.

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arXiv2013

A Mathematical Model for an Hourglass Magnetic Field

Starting with a mathematical boundary value problem for the magnetic vector potential in an axisymmetric cylindrical coordinate system, we derive a general solution for any arbitrary current distribution using the method of Green's functions. We use this to derive an analytic form for an hourglass magnetic field pattern created by electrical currents that are concentrated near (but not confined within) the equatorial plane of a cylindrical coordinate system. Our solution is not characterized by a cusp at the equatorial plane, as in previous solutions based on a current sheet. The pattern we derive provides a very good fit to hourglass magnetic field patterns emerging from three-dimensional numerical simulations of core formation, and can in principle be used for source-fitting of observed magnetic hourglass patterns.

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arXiv2013

The Effect of Magnetic Fields and Ambipolar Diffusion on Core Mass Functions

Linear analysis of the formation of protostellar cores in planar magnetic interstellar clouds yields information about length scales involved in star formation. Combining these length scales with various distributions of other environmental variables, (i.e., column density and mass-to-flux ratio) and applying Monte Carlo methods allow us to produce synthetic core mass functions (CMFs) for different environmental conditions. Our analysis shows that the shape of the CMF is directly dependent on the physical conditions of the cloud. Specifically, magnetic fields act to broaden the mass function and develop a high-mass tail while ambipolar diffusion will truncate this high-mass tail. In addition, we analyze the effect of small number statistics on the shape and high-mass slope of the synthetic CMFs. We find that observed core mass functions are severely statistically limited, which has a profound effect on the derived slope for the high-mass tail.

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arXiv2012

The Migrating Embryo Model for Disk Evolution

A new view of disk evolution is emerging from self-consistent numerical simulation modeling of the formation of circumstellar disks from the direct collapse of prestellar cloud cores. This has implications for many aspects of star and planet formation, including the growth of dust and high-temperature processing of materials. A defining result is that the early evolution of a disk is crucially affected by the continuing mass loading from the core envelope, and is driven into recurrent phases of gravitational instability. Nonlinear spiral arms formed during these episodes fragment to form gaseous clumps in the disk. These clumps generally migrate inward due to gravitational torques arising from their interaction with a trailing spiral arm. Occasionally, a clump can open up a gap in the disk and settle into a stable orbit, revealing a direct pathway to the formation of companion stars, brown dwarfs, or giant planets. At other times, when multiple clumps are present, a low mass clump may even be ejected from the system, providing a pathway to the formation of free-floating brown dwarfs and giant planets in addition to low mass stars. Finally, it has been suggested that the inward migration of gaseous clumps can provide the proper conditions for the transport of high-temperature processed solids from the outer disk to the inner disk, and even possibly accelerate the formation of terrestrial planets in the inner disk. All of these features arising from clump formation and migration can be tied together conceptually in a Migrating Embryo model for disk evolution that can complement the well-known Core Accretion model for planet formation.

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arXiv2012

Two-Stage Fragmentation for Cluster Formation: Analytical Model and Observational Considerations

Linear analysis of the formation of protostellar cores in planar magnetic interstellar clouds shows that molecular clouds exhibit a preferred length scale for collapse that depends on the mass-to-flux ratio and neutral-ion collision time within the cloud. We extend this linear analysis to the context of clustered star formation. By combining the results of the linear analysis with a realistic ionization profile for the cloud, we find that a molecular cloud may evolve through two fragmentation events in the evolution toward the formation of stars. Our model suggests that the initial fragmentation into clumps occurs for a transcritical cloud on parsec scales while the second fragmentation can occur for transcritical and supercritical cores on subparsec scales. Comparison of our results with several star forming regions (Perseus, Taurus, Pipe Nebula) shows support for a two-stage fragmentation model.

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arXiv2012

The Ejection of Low Mass Clumps During Star Formation

Modeling of the self-consistent formation and evolution of disks as a result of prestellar core collapse reveals an intense early phase of recurrent gravitational instability and clump formation. These clumps generally migrate inward due to gravitational interaction with trailing spiral arms, and can be absorbed into the central object. However, in situations of multiple clump formation, gravitational scattering of clumps can result in the ejection of a low mass clump. These clumps can then give rise to free-floating low mass stars, brown dwarfs, or even giant planets. Detailed modeling of this process in the context of present-day star formation reveals that these clumps start out essentially as Larson first cores and grow subsequently by accretion. In the context of Pop III star formation, preliminary indications are that the disk clumps may also be of low mass. This mechanism of clump formation and possible ejection provides a channel for the formation of low mass objects in the first generation of stars.

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arXiv2012

Bridging the gap: disk formation in the Class 0 phase with ambipolar diffusion and Ohmic dissipation

Context: Ideal MHD simulations have revealed catastrophic magnetic braking (MB) in the protostellar phase, which prevents the formation of a centrifugal disk around a nascent protostar. Aims: We determine if non-ideal MHD, including the effects of ambipolar diffusion and Ohmic dissipation determined from a detailed chemical network model, allows for disk formation at the earliest stages of star formation (SF). Methods: We employ the axisymmetric thin-disk approximation in order to resolve a dynamic range of 9 orders of magnitude in length and 16 in density, while also calculating partial ionization using up to 19 species in a detailed chemical equilibrium model. MB is applied using a steady-state approximation, and a barotropic relation is used to capture the thermal evolution. Results: We resolve the formation of the first and second cores, with expansion waves at the periphery of each, a magnetic diffusion shock, and prestellar infall profiles at larger radii. Power-law profiles in each region can be understood analytically. After the formation of the second core, centrifugal support rises rapidly and a low-mass disk of radius ~10 R_Sun is formed, when the second core has mass ~0.001 M_Sun. The mass-to-flux ratio is ~10,000 times the critical value in the central region. Conclusions: A small centrifugal disk can form in the earliest stage of SF, due to a shut-off of MB caused by magnetic field dissipation in the first core region. There is enough angular momentum loss to allow the second collapse to occur directly, and a low-mass stellar core to form with a surrounding disk. The disk mass and size will depend upon how the angular momentum transport mechanisms within the disk can keep up with mass infall onto the disk. We estimate that the disk will remain <~10 AU, undetectable even by ALMA, in the early Class 0 phase.

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arXiv2012

A Hybrid Scenario for the Formation of Brown Dwarfs and Very Low Mass Stars

We present a calculation of protostellar disk formation and evolution in which gaseous clumps (essentially, the first Larson cores formed via disk fragmentation) are ejected from the disk during the early stage of evolution. This is a universal process related to the phenomenon of ejection in multiple systems of point masses. However, it occurs in our model entirely due to the interaction of compact, gravitationally-bound gaseous clumps and is free from the smoothing-length uncertainty that is characteristic of models using sink particles. Clumps that survive ejection span a mass range of 0.08--0.35 $M_\odot$, and have ejection velocities $0.8 \pm 0.35$ km s$^{-1}$, which are several times greater than the escape speed. We suggest that, upon contraction, these clumps can form substellar or low-mass stellar objects with notable disks, or even close-separation very-low-mass binaries. In this hybrid scenario, allowing for ejection of clumps rather than finished protostars/proto--brown-dwarfs, disk formation and the low velocity dispersion of low-mass objects are naturally explained, while it is also consistent with the observation of isolated low-mass clumps that are ejection products. We conclude that clump ejection and the formation of isolated low mass stellar and substellar objects is a common occurrence, with important implications for understanding the initial mass function, the brown dwarf desert, and the formation of stars in all environments and epochs.

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arXiv2011

Magnetic Field Diffusion and the Formation of Circumstellar Disks

A non-ideal MHD collapse calculation employing the axisymmetric thin-disk approximation is used to resolve cloud core collapse down to the scales of the second (stellar) core. Rotation and a magnetic braking torque are included in the model, and the partial ionization resulting in ambipolar diffusion and Ohmic dissipation is calculated from a detailed chemical network. We find that a centrifugal disk can indeed form in the earliest stage of star formation, due to a shut-off of magnetic braking caused by magnetic field diffusion in the first core region. Thus, there is no catastrophic magnetic braking in a model with realistic non-ideal MHD.

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arXiv2010

Formation of collapsing cores in subcritical magnetic clouds: three-dimensional MHD simulations with ambipolar diffusion

We employ the three-dimensional magnetohydrodynamic simulation including ambipolar diffusion to study the gravitationally-driven fragmentation of subcritical molecular clouds, in which the gravitational fragmentation is stabilized as long as magnetic flux-freezing applies. The simulations show that the cores in an initially subcritical cloud generally develop gradually over an ambipolar diffusion time, which is about a few $\times 10^7$ years in a typical molecular cloud. On the other hand, the formation of collapsing cores in subcritical clouds is accelerated by supersonic nonlinear flows. Our parameter study demonstrates that core formation occurs faster as the strength of the initial flow speed in the cloud increases. We found that the core formation time is roughly proportional to the inverse of the square root of the enhanced density created by the supersonic nonlinear flows. The density dependence is similar to that derived in quasistatically contracting magnetically supported clouds, although the core formation conditions are created by the nonlinear flows in our simulations. We have also found that the accelerated formation time is not strongly dependent on the initial strength of the magnetic field if the cloud is highly subcritical. Our simulation shows that the core formation time in our model subcritical clouds is several $\times 10^6$ years, due to the presence of large-scale supersonic flows ($\sim 3$ times sound speed). Once a collapsing core forms, the density, velocity, and magnetic field structure of the core does not strongly depend on the initial strength of the velocity fluctuation. The infall velocities of the cores are subsonic and the magnetic field lines show weak hourglass shapes.

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