arXiv subjects

Shantanu Basu

Publications and source records attributed to Shantanu Basu.

At least 37 records · Page 2Linked to original sources

arXiv2022

A semi-analytic model for the temporal evolution of the episodic disc-to-star accretion rate during star formation

We develop a semi-analytic formalism for the determination of the evolution of the stellar mass accretion rate for specified density and velocity profiles that emerge from the runaway collapse of a prestellar cloud core. In the early phase, when the infall of matter from the surrounding envelope is substantial, the star accumulates mass primarily because of envelope-induced gravitational instability in a protostellar disc. In this phase, we model the envelope mass accretion rate from the isothermal free-fall collapse of a molecular cloud core. The disc gains mass from the envelope, and transports matter to the star via a disc accretion mechanism that includes episodic gravitational instability and mass accretion bursts according to the Toomre $Q$-criterion. In a later phase, mass is accreted on to the star due to gravitational torques within the spiral structures in the disc, in a manner that analytic theory suggests has a mass accretion rate $\propto t^{-6/5}$. Our model provides a self-consistent evolution of the mass accretion rate by joining the spherical envelope accretion (dominant at the earlier stage) with the disc accretion (important at the later stage), and accounts for the presence of episodic accretion bursts at appropriate times. We show using a simple example that the burst mode can provide a good match to the observed distribution of bolometric luminosities. Our framework reproduces key elements of detailed numerical simulations of disc accretion and can aid in developing intuition about the basic physics as well as to compare theory with observations.

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arXiv2022

The Magnetic Field versus Density relation in Star-Forming Molecular Clouds

We study the magnetic field to density ($B-ρ$) relation in turbulent molecular clouds with dynamically important magnetic fields using nonideal three-dimensional magnetohydrodynamic simulations. Our simulations show that there is a distinguishable break density $ρ_{\rm T}$ between the relatively flat low density regime and a power-law regime at higher densities. We present an analytic theory for $ρ_{\rm T}$ based on the interplay of the magnetic field, turbulence, and gravity. The break density $ρ_{\rm T}$ scales with the strength of the initial Alfvén Mach number $\mathcal{M}_{\rm A0}$ for sub-Alfvénic ( $\mathcal{M}_{\rm A0}<1$) and trans-Alfvénic ($\mathcal{M}_{\rm A0} \sim 1$) clouds. We fit the variation of $ρ_{\rm T}$ for model clouds as a function of $\mathcal{M}_{\rm A0}$, set by different values of initial sonic Mach number $\mathcal{M_{\rm 0}}$ and the initial ratio of gas pressure to magnetic pressure $β_{\rm 0}$. This implies that $ρ_{\rm T}$, which denotes the transition in mass-to-flux ratio from the subcritical to supercritical regime, is set by the initial turbulent compression of the molecular cloud.

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arXiv2021

Hourglass Magnetic Field from a Survey of Current Density Profiles

Modelling the magnetic field in prestellar cores can serve as a useful tool for studying the initial conditions of star formation. The analytic hourglass model of Ewertowski and Basu (2013) provides a means to fit observed polarimetry measurements and extract useful information. The original model does not specify any radial distribution of the electric current density. Here, we perform a survey of possible centrally-peaked radial distributions of the current density, and numerically derive the full hourglass patterns. Since the vertical distribution is also specified in the original model, we can study the effect of different ratios of vertical to radial scale length on the overall hourglass pattern. Different values of this ratio may correspond to different formation scenarios for prestellar cores. We demonstrate the flexibility of our model and how it can be applied to a variety of magnetic field patterns.

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arXiv2021

Supermassive Star Formation in Magnetized Atomic-Cooling Gas Clouds: Enhanced Accretion, Intermittent Fragmentation, and Continuous Mergers

The origin of supermassive black holes (with $\gtrsim\!10^9\,M_{\odot}$) in the early universe (redshift $z \sim 7$) remains poorly understood. Gravitational collapse of a massive primordial gas cloud is a promising initial process, but theoretical studies have difficulty growing the black hole fast enough. We focus on the magnetic effects on star formation that occurs in an atomic-cooling gas cloud. Using a set of three-dimensional magnetohydrodynamic (MHD) simulations, we investigate the star formation process in the magnetized atomic-cooling gas cloud with different initial magnetic field strengths. Our simulations show that the primordial magnetic seed field can be quickly amplified during the early accretion phase after the first protostar formation. The strong magnetic field efficiently extracts angular momentum from accreting gas and increases the accretion rate, which results in the high fragmentation rate in the gravitationally unstable disk region. On the other hand, the coalescence rate of fragments is also enhanced by the angular momentum transfer due to the magnetic effects. Almost all the fragments coalesce to the primary star, so the mass growth rate of the massive star increases due to the magnetic effects. We conclude that the magnetic effects support the direct collapse scenario of supermassive star formation.

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arXiv2021

The Mass Function of Supermassive Black Holes in the Direct-collapse Scenario

One of the ideas to explain the existence of supermassive black holes (SMBH) that are in place by z~7 is that there was an earlier phase of very rapid accretion onto direct collapse black holes (DCBH) that started their lives with masses ~ 10^4-10^5 M_solar. Working in this scenario, we show that the mass function of SMBH after such a limited time period with growing formation rate paired with super-Eddington accretion can be described as a broken power-law with two characteristic features. There is a power-law at intermediate masses whose index is the dimensionless ratio α = λ/γ, where λ is the growth rate of the number of DCBH during their formation era, and γ is the growth rate of DCBH masses by super-Eddington accretion during the DCBH growth era. A second feature is a break in the power law profile at high masses, above which the mass function declines rapidly. The location of the break is related to the dimensionless number \b{eta} = γ T, where T is the duration of the period of DCBH growth. If the SMBH continue to grow at later times at an Eddington-limited accretion rate, then the observed quasar luminosity function can be directly related to the tapered power-law function derived in this paper.

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arXiv2021

Effect of mass loss due to stellar winds on the formation of supermassive black hole seeds in dense nuclear star clusters

The observations of high redshifts quasars at $z\gtrsim 6$ have revealed that supermassive black holes (SMBHs) of mass $\sim 10^9\,\mathrm{M_{\odot}}$ were already in place within the first $\sim$ Gyr after the Big Bang. Supermassive stars (SMSs) with masses $10^{3-5}\,\mathrm{M_{\odot}}$ are potential seeds for these observed SMBHs. A possible formation channel of these SMSs is the interplay of gas accretion and runaway stellar collisions inside dense nuclear star clusters (NSCs). However, mass loss due to stellar winds could be an important limitation for the formation of the SMSs and affect the final mass. In this paper, we study the effect of mass loss driven by stellar winds on the formation and evolution of SMSs in dense NSCs using idealised N-body simulations. Considering different accretion scenarios, we have studied the effect of the mass loss rates over a wide range of metallicities $Z_\ast=[.001-1]\mathrm{Z_{\odot}}$ and Eddington factors $f_{\rm Edd}=L_\ast/L_{\mathrm{Edd}}=0.5,0.7,\,\&\, 0.9$. For a high accretion rate of $10^{-4}\,\mathrm{M_{\odot}yr^{-1}}$, SMSs with masses $\gtrsim 10^3\MSun$ could be formed even in a high metallicity environment. For a lower accretion rate of $10^{-5}\,\mathrm{M_{\odot}yr^{-1}}$, SMSs of masses $\sim 10^{3-4}\,\mathrm{M_{\odot}}$ can be formed for all adopted values of $Z_\ast$ and $f_{\rm Edd}$, except for $Z_\ast=\mathrm{Z_{\odot}}$ and $f_{\rm Edd}=0.7$ or 0.9. For Eddington accretion, SMSs of masses $\sim 10^3\,\mathrm{M_{\odot}}$ can be formed in low metallicity environments with $Z_\ast\lesssim 0.01\mathrm{Z_{\odot}}$. The most massive SMSs of masses $\sim 10^5\,\mathrm{M_{\odot}}$ can be formed for Bondi-Hoyle accretion in environments with $Z_\ast \lesssim 0.5\mathrm{Z_{\odot}}$.

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arXiv2021

Variation of the Core Lifetime and Fragmentation Scale in Molecular Clouds as an Indication of Ambipolar Diffusion

Ambipolar diffusion likely plays a pivotal role in the formation and evolution of dense cores in weakly-ionized molecular clouds. Linear analyses show that the evolutionary times and fragmentation scales are significantly greater than the hydrodynamic (Jeans) values even for clouds with mildly supercritical mass-to-flux ratio. We utilize values of fragmentation scales and growth times that correspond to typical ionization fractions within a molecular cloud, and apply to the context of the observed estimated lifetime of prestellar cores as well as the observed number of such embedded cores forming in a parent clump. By varying a single parameter, the mass-to-flux ratio, over the range of observationally measured densities, we fit the range of estimated prestellar core lifetimes ($\sim 0.1$ to a few Myr) identified with Herschel as well as the number of embedded cores formed in a parent clump measured in Perseus with the Submillimeter Array (SMA). Our model suggests that the prestellar cores are formed with a transcritical mass-to-flux ratio and higher densities correspond to somewhat higher mass-to-flux ratio but the normalized mass-to-flux ratio $μ$ remains in the range $1 \lesssim μ\lesssim 2$. Our best-fit model exhibits $B \propto n^{0.43}$ for prestellar cores, due to partial flux-freezing as a consequence of ambipolar diffusion.

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arXiv2021

Magnetic Properties of Star-Forming Dense Cores

Magnetic and energetic properties are presented for 17 dense cores within a few hundred pc of the Sun. Their plane-of-sky field strengths are estimated from the dispersion of polarization directions, following Davis, Chandrasekhar and Fermi (DCF). Their ratio of mass to magnetic critical mass is 0.5-3, indicating nearly critical field strengths. The field strength B_pos is correlated with column density N as B_pos~N^p, where p=1.05+-0.08, and with density n as B_pos~n^q, where q=0.66+-0.05. These magnetic properties are consistent with those derived from Zeeman studies (Crutcher et al. 2010), with less scatter. Relations between virial mass M_V, magnetic critical mass M_B, and Alfven amplitude sigma_B/B match the observed range of M/M_B for cores observed to be nearly virial, with M/M_V=0.5-2, with moderate Alfven amplitudes, and with sigma_B/B=0.1-0.4. The B-N and B-n correlations in the DCF and Zeeman samples can be explained when such bound, Alfvenic, and nearly-critical cores have central concentration and spheroidal shape. For these properties, B~N because M/M_B is nearly constant compared to the range of N, and B~n^(2/3) because M^(1/3) is nearly constant compared to the range of n^(2/3). The observed core fields which follow B~n^(2/3) need not be much weaker than gravity, in contrast to core fields which follow B~n^(2/3) due to spherical contraction at constant mass (Mestel 1966). Instead, the nearly critical values of M/M_B suggest that the observed core fields are nearly as strong as possible, among values which allow gravitational contraction.

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arXiv2021

Linear Stability Analysis of a Magnetic Rotating Disk with Ohmic Dissipation and Ambipolar Diffusion

We perform a linear analysis of the stability of isothermal, rotating, magnetic, self-gravitating sheets that are weakly ionized. The magnetic field and rotation axis are perpendicular to the sheet. We include a self-consistent treatment of thermal pressure, gravitational, rotational, and magnetic (pressure and tension) forces together with two nonideal magnetohydrodynamic (MHD) effects (Ohmic dissipation and ambipolar diffusion) that are treated together for their influence on the properties of gravitational instability for a rotating sheet-like cloud or disk. Our results show that there is always a preferred length scale and associated minimum timescale for gravitational instability. We investigate their dependence on important dimensionless free parameters of the problem: the initial normalized mass-to-flux ratio $μ_0$, the rotational Toomre parameter $Q$, the dimensionless Ohmic diffusivity $\tildeη_{\rm OD,0}$, and the dimensionless neutral-ion collision time $\tildeτ_{\rm{ni,0}}$ that is a measure of the ambipolar diffusivity. One consequence of $\tildeη_{\rm OD,0}$ is that there is a maximum preferred lengthscale of instability that occurs in the transcritical ($μ_0 \gtrsim 1$) regime, qualitatively similar to the effect of $\tildeτ_{\rm{ni,0}}$, but with quantitative differences. The addition of rotation leads to a generalized Toomre criterion (that includes a magnetic dependence) and modified lengthscales and timescales for collapse. When nonideal MHD effects are also included, the Toomre criterion reverts back to the hydrodynamic value. We apply our results to protostellar disk properties in the early embedded phase and find that the preferred scale of instability can significantly exceed the thermal (Jeans) scale and the peak preferred fragmentation mass is likely to be $\sim 10- 90 \ M_{\rm Jup}$.

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arXiv2021

Fitting an Analytic Magnetic Field to a Prestellar Core

We deploy and demonstrate the capabilities of the magnetic field model developed by Ewertowski & Basu (2013) by fitting observed polarimetry data of the prestellar core FeSt 1-457. The analytic hourglass magnetic field function derived directly from Maxwell's equations yields a central-to-surface magnetic field strength ratio in the equatorial plane, as well as magnetic field directions with relative magnitudes throughout the core. This fit emerges from a comparison of a single plane of the model with the polarization map that results from the integrated properties of the magnetic field and dust throughout the core. Importantly, our fit is independent of any assumed density profile of the core. We check the robustness of the fit by using the POLARIS code to create synthetic polarization maps that result from the integrated scattering and emission properties of the dust grains and their radiative transfer, employing an observationally-motivated density profile. We find that the synthetic polarization maps obtained from the model also provides a good fit to the observed polarimetry. Our model fits the striking feature of significant curvature of magnetic field lines in the outer part of FeSt 1-457. Combined with independent column density estimates, we infer that the core of size $R_{\rm gas}$ has a mildly supercritical mass-to-flux ratio and may have formed through dynamical motions starting from a significantly larger radius $R$. A breakdown of flux-freezing through neutral-ion slip (ambipolar diffusion) could be responsible for effecting such a transition from a large-scale magnetic field structure to a more compact gas structure.

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arXiv2020

Accretion bursts in magnetized gas-dust protoplanetary disks

Aims and Methods. Accretion bursts triggered by the magnetorotational instability (MRI) in the innermost disk regions were studied for protoplanetary gas-dust disks formed from prestellar cores of various mass $M_{\rm core}$ and mass-to-magnetic flux ratio $λ$. Numerical magnetohydrodynamics simulations in the thin-disk limit were employed to study the long-term ($\sim 1.0$~Myr) evolution of protoplanetary disks with an adaptive turbulent $α$-parameter, which depends explicitly on the strength of the magnetic field and ionization fraction in the disk. The numerical models also feature the co-evolution of gas and dust, including the back-reaction of dust on gas and dust growth. Results. Dead zone with a low ionization fraction $x <= 10^{-13}$ and temperature on the order of several hundred Kelvin forms in the inner disk soon after its formation, extending from several to several tens of astronomical units depending on the model. The dead zone features pronounced dust rings that are formed due to the concentration of grown dust particles in the local pressure maxima. Thermal ionization of alkaline metals in the dead zone trigger the MRI and associated accretion burst, which is characterized by a sharp rise, small-scale variability in the active phase, and fast decline once the inner MRI-active region is depleted of matter. The burst occurrence frequency is highest in the initial stages of disk formation, and is driven by gravitational instability (GI), but declines with diminishing disk mass-loading from the infalling envelope. There is a causal link between the initial burst activity and the strength of GI in the disk fueled by mass infall from the envelope. Abridged.

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arXiv2020

The Effect of Misalignment between Rotation Axis and Magnetic Field on Circumstellar Disk

The formation of circumstellar disks is investigated using three-dimensional resistive magnetohydrodynamic simulations, in which the initial prestellar cloud has a misaligned rotation axis with respect to the magnetic field. We examine the effects of (i) the initial angle difference between the global magnetic field and the cloud rotation axis ($θ_0$) and (ii) the ratio of the thermal to gravitational energy ($α_0$). We study $16$ models in total and calculate the cloud evolution until $\sim \! 5000$ yr after protostar formation. Our simulation results indicate that an initial non-zero $θ_0$ ($> 0$) promotes the disk formation but tends to suppress the outflow driving, for models that are moderately gravitationally unstable, $α_0 \lesssim 1$. In these models, a large-sized rotationally-supported disk forms and a weak outflow appears, in contrast to a smaller disk and strong outflow in the aligned case ($θ_0 = 0$). Furthermore, we find that when the initial cloud is highly unstable with small $α_0$, the initial angle difference $θ_0$ does not significantly affect the disk formation and outflow driving.

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arXiv2020

Using the Modified Lognormal Power Law Distribution to Model the Mass Function of NGC 1711

A determination of the mass function (MF) of stellar clusters can be quite dependent on the range of measured masses, the fitting technique, and the analytic function that is being fit to the data. Here, we use HST/WFPC2 data of NGC 1711, a stellar cluster in the Large Magellanic Cloud, as a test case to explore a range of possible determinations of the MF from a single dataset. We employ the analytic modified lognormal power-law (MLP) distribution, a hybrid function that has a peaked lognormal-like body and a power-law tail at intermediate and high masses. A fit with the MLP has the advantage that the resulting best-fit function can be either a hybrid function, a pure lognormal, or a pure power law, in different limits of the function. The completeness limit for the observations means that the data contains masses above $\sim 0.90\,M_{\odot}$. In this case, the MLP fits yield essentially a pure power-law MF. We demonstrate that the nonlinear regression/least-squares approach is not justified since the underlying assumptions are not satisfied. By using maximum likelihood estimation, which is independent of binning, we find a best-fit functional form $dN/d\ln m \propto m^{-α}$, where $α= 1.72 \pm 0.05$ or $1.75 \pm 0.05$ for two different theoretical isochrone models, respectively. Furthermore, we explore the possibility of systematic errors in the determination of the power-law index due to the depth of the observations. When we combine the observational data with artificially generated data from the lognormal Chabrier IMF for masses below $0.90\, M_{\odot}$, the best fit MLP is a hybrid function but with a steeper asymptotic slope i.e., $α= 2.04 \pm 0.07$. This illustrates the systematic uncertainties in commonly used MF parameters that can depend on the range of data that is fitted.

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arXiv2020

Magnetic Field Structure in Spheroidal Star-Forming Clouds. II. Estimating Field Structure from Observed Maps

This paper presents models to estimate the structure of density and magnetic field strength in spheroidal condensations, from maps of their column density and their polarization of magnetically aligned dust grains. The density model is obtained by fitting a column density map with an embedded p = 2 Plummer spheroid of any aspect ratio and inclination. The magnetic properties are based on the density model, on the Davis-Chandrasekhar-Fermi (DCF) model of Alfvénic fluctuations, and on the Spheroid Flux Freezing (SFF) model of mass and flux conservation in Paper I. The field strength model has the resolution of the column density map, which is finer than the resolution of the DCF estimate of field strength. The models are applied to ALMA observations of the envelope of the protostar BHR71 IRS1. Column density fits give the density model, from (2.0 +- 0.4) x 10^5 cm^-3 to (7 +- 1) x 10^7 cm^-3 . The density model predicts the field directions map, which fits the polarization map best within 1100 au, with standard deviation of angle differences 17°. In this region the DCF mean field strength is 0.7 +- 0.2 mG and the envelope mass is supercritical, with ratio of mass to magnetic critical mass 1.5 +- 0.4. The SFF field strength profile scales with the DCF field strength, from 60 x 10μG to 4+-1 mG. The spatial resolution of the SFF field strength estimate is finer than the DCF resolution by a factor ~7, and the peak SFF field strength exceeds the DCF field strength by a factor ~5.

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arXiv2020

A Multiple Power Law Distribution for Initial Mass Functions

We introduce a new multi-power-law distribution for the Initial Mass Function (IMF) to explore its potential properties. It follows on prior work that introduced mechanisms accounting for mass accretion in star formation, developed within the framework of general evolution equations for the mass distribution of accreting and non-accreting (proto)stars. This paper uses the same fundamental framework to demonstrate that the interplay between a mass-dependent and a time-dependent step-like dropout rate from accretion leads to IMFs that exhibit multiple power laws for an exponential mass growth. While the mass-dependent accretion and its dropout is intrinsic to each star, the time-dependent dropout might be tied to a specific history such as the rapid consumption of nebular material by nearby stars or the sweeping away of some material by shock waves. The time-dependent dropout folded into the mass-dependent process of star formation is shown to have a significant influence on the IMFs.

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arXiv2020

Different Modes of Star Formation II: Gas Accretion Phase of Initially Subcritical Star-Forming Clouds

The accretion phase of star formation is investigated in magnetically-dominated clouds that have an initial subcritical mass-to-flux ratio. We employ nonideal magnetohydrodynamic simulations that include ambipolar diffusion and ohmic dissipation. During the early prestellar phase the mass-to-flux ratio rises toward the critical value for collapse, and during this time the angular momentum of the cloud core is reduced significantly by magnetic braking. Once a protostar is formed in the core, the accretion phase is characterized by the presence of a small amount of angular momentum but a large amount of magnetic flux in the near-protostellar environment. The low angular momentum leads to a very small (or even nonexistent) disk and weak outflow, while the large magnetic flux can lead to an interchange instability that rapidly removes flux from the central region. The effective magnetic braking in the early collapse phase can even lead to a counter-rotating disk and outflow, in which the rotation direction of the disk and outflow is opposite to that of the infalling envelope. The solutions with a counter-rotating disk, tiny disk, or nonexistent disk (direct collapse) are unique outcomes that are realized in collapse from magnetically-dominated clouds with an initial subcritical mass-to-flux ratio.

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arXiv2019

The Formation of Stars -- From Filaments to Cores to Protostars and Protoplanetry Disks

Star formation involves the flow of gas and dust within molecular clouds into protostars and young stellar objects (YSOs) due to gravity. Along the way, these flows are shaped significantly by many other mechanisms, including pressure, turbulent motions, magnetic fields, stellar feedback, jets, and angular momentum. How all these mechanisms interact nonlinearly with each other on various length scales leads to the formation and evolution of substructures within clouds, including filaments, clumps, cores, disks, outflows, the protostars/YSOs themselves, and planets. In this white paper, prepared for the 2020 Long Range Plan panel which will recommend Canada's future directions for astronomy, we describe the observational and theoretical leadership in the star formation field that Canada's vibrant community has demonstrated over the past decade. Drawing from this extensive background, we identify five key questions that must be addressed for further progress to be made in understanding star formation in the next decade. Addressing these questions will improve our understanding of the dynamics of the dense gas and the role of the magnetic field in star formation, the optical properties of the dust used to trace mass and magnetic fields, the sources of variability in star-forming objects on short timescales, and the physical processes that specifically promote the clustering of stars. We further highlight key facilities in which Canada should become involved to continue making progress in this field. Single-dish facilities we recommend include LSST, trans-atmospheric far-infrared telescopes like BLAST-TNG and SPICA, and ground-based telescopes like JCMT, GBT, and CCAT-p. Interferometric facilities we recommend include ALMA, ngVLA, and SKA1.

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arXiv2019

The Transition from a Lognormal to a Power-Law Column Density Distribution in Molecular Clouds: An Imprint of the Initial Magnetic Field and Turbulence

We introduce a theory for the development of a transitional column density $Σ_{\rm TP}$ between the lognormal and the power-law forms of the probability distribution function (PDF) in a molecular cloud. Our turbulent magnetohydrodynamic simulations show that the value of $Σ_{\rm TP}$ increases as the strength of both the initial magnetic field and turbulence increases. We develop an analytic expression for $Σ_{\rm TP}$ based on the interplay of turbulence, a (strong) magnetic field, and gravity. The transition value $Σ_{\rm TP}$ scales with $\mathcal{M}^2_{\rm 0}$, the square of the initial sonic Mach number, and $β_{0}$, the initial ratio of gas pressure to magnetic pressure. We fit the variation of $Σ_{\rm TP}$ among different model clouds as a function of $\mathcal{M}^2_{\rm 0} β_{0}$, or equivalently the square of the initial Alfvénic Mach number $\mathcal{M}^2_{\rm A0}$. This implies that the transition value $Σ_{\rm TP}$ is an imprint of cloud initial conditions and is set by turbulent compression of a magnetic cloud. Physically, the value of $Σ_{\rm TP}$ denotes the boundary above which the mass-to-flux ratio becomes supercritical and gravity drives the evolution.

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